VENICE – Venice festival scheduling is a business that can seem haphazard at best, and perverse at worst. Kim Ki-duk’s castration-and-incest bonanza “Moebius” straight after breakfast? Sure. Philip Groning’s three-hour, 59-chapter dissection of domestic abuse to finish the day? Hey, why not? Sometimes, however, they let on that they really know what they’re doing with a juxtaposition that seems too perfect to be accidental — and they don’t come much more effectively on-the-nose than last night’s back-to-back double bill of Alex Gibney’s “The Armstrong Lie” (B-) and Errol Morris’ “The Unknown Known” (C+). (Even the titles have a pleasingly similar cadence.) It wasn’t labelled in the programme as The Great American Douchebags Special, but we got the idea.

Perhaps it’s a side effect of viewing them with only a 20-minute, theater-traversing in between, but the films seemed too well-matched — not just in content, but in a number of their strongest and weakest points — to review separately, even if they’ll rarely be re-partnered outside the festival environment.

Of course, it’d be a pretty vapid line of criticism to directly equate the docs’ subjects. Having finally admitted guilt after years of strenuously denied doping allegations — and having been unceremoniously stripped of his record seven Tour de France titles — cyclist Lance Armstrong may be the biggest fraud in the history of recorded sport, but his sins have largely come at his own expense. That’s something that can’t be said for former US Secretary of Defense Donald Rumsfeld, whose strenuously denied errors of judgement in the Iraq War came not only at significant human cost, but at the already frail international political credibility of his country. Degrees of media fascination may suggest otherwise, but one is plainly a drop in the ocean of another.

What they have in common — and what seems principally to aggravate Gibney and Morris, both occasionally audible in their films as rather animated interviewers — is a certain faith-breaking status in contemporary American culture, a legacy of public distrust that, particularly in the case of a more romantic figure like Armstrong, has been symbolically extrapolated to realms beyond their personal reach. Rumsfeld certainly wasn’t the only one making terrible, uninformed decisions in that fraught period of US political history, but for a few years, it seemed his thin smile and rimless spectacles were the all-purpose face of American institutional corruption — arguably even more so than his equally widely loathed Commander-in-Chief George W. Bush, if only because Rumsfeld was so much more articulate, and therefore more insidious to his detractors.

Armstrong, by contrast, has no political agency, but his long-term feat of self-elevating deception — perhaps more immediately comprehensible to the general public in terms of its moral transgressions than Rumsfeld’s political acts, and more prone to salacious media interpretations — betrayed an ideal of American heroism that the global public had invested in to a considerable degree. Nobody expects politicians, even the ones on the side of right, to be all that honorable. (We do, however, want them to be competent.) But the good-looking cancer survivor who battles the odds to become a world-beating athlete and lead-by-example philanthropist? When he turns out to be an illusion, nobody dies — but people are hurt anyway.

Gibney is one of those people. Normally the coolest of customers, the prolific documentarian here lets a passive-aggressive tone of disenchantment, even anger, seep into his filmmaking that speaks less of a admirer’s aggrievement than of a professional’s annoyance at having had the wool pulled over his eyes. Gibney started this documentary with a very different motivation in 2009, chronicling Armstrong’s attempted Tour de France comeback — regardless of the outcome, his last professional hurrah before he was conclusively rumbled as a doper — with the intention of discovering just what made this supposed human superman tick.

It’d have been an unconventionally rose-tinted approach for the usually assidious Gibney; several talking heads in the film’s 2013 sections, including Armstrong’s former teammate Frankie Andreu and his wife, dogged Armstrong persecutor Betsy, openly express their amused dismay that he ever considered making it. But Gibney admits that, four years ago, he fell hook, line and sinker for the so-called Armstrong lie, and has had to perform an about-face on this entire project and his reason for making it.

That can’t be an easy admission to make: the resulting peevishness of “The Armstrong Lie” makes it at once one of Gibney’s most humanly compelling works, and one of his more rhetorically inconsistent, as the film unavoidably slides between interview footage from before and after the fact that pursues very different intelligence and emotion.

Armstrong is a chilly but willing interview participant in footage filmed this spring, in the aftermath of his irreversibly comprehensive Oprah confession, but strangely, he never seems more contrite than in intimate, conversational footage with Gibney immediately after his 2009 Tour defeat, in which he apologizes for losing and thereby denying Gibney’s film its triumphant ending. He’s not joking, either. All along, Armstrong’s chief skill — well, maybe not his chief one; he’s still a half-decent cyclist — has been as a builder of personal narrative. If he’s unrewardingly bland and unforthcoming in what should be the ‘gotcha!’ stages of Gibney’s new-model film, it’s because, with his personal and professional reputation still in fresh tatters, he hasn’t located the next narrative yet.

Rumsfeld, by contrast, built an entire career on being unrewardingly bland and unforthcoming — as “The Unknown Known” reminds us with frequent flashbacks (boxed, as we saw them, within a turn-of-the-century television screen) to his famous White House press conferences, where he deflected one question after another with breathtakingly smarmy poise and patter. He may not have fooled onlookers into believing he knew significantly more than they did — or, in the case of his recurring gaffe over WMDs, that his professed ignorance was any more considered than theirs — but his watery confidence was intimidating on a human level. It’s hard to argue productively with someone who may indeed have nothing to hide, who genuinely appears to believe his stubborn, transparently unsustainable convictions.

That enigma — whether Rumsfeld has ever doubted his public frontage, whether his most contentious war strategies were born of profound belief or tactical stopgapping — is one Errol Morris doesn’t really come close to penetrating in “The Unknown Known.” A typically handsome, charcoal-hued effort, it has plainly been conceived as a structural and thematic bookend to “The Fog of War,” Morris’ Oscar-winning interrogation of another former Defence Secretary, Robert McNamara, with a lot on his conscience. In his smooth but insistent way, Morris cracked McNamara: there was no cathartic mea culpa on his Vietnam decision-making, of course, but his open engagement and reasonably candid self-evaluation was victory enough.

If Morris was hoping to tease out this degree of consideration in Rumsfeld, he’s out of luck. Pristinely power-suited, with his high, even vocal tone as intact as if he’d just fielded another press conference, Rumsfeld sits before Morris’ classically direct camera like a man out to pass a test, barely pausing for thought before batting off the interviewer’s questions with unfazed, occasionally bored politeness. “I’m not an obsessive person,” he responds dully, at the first hint of a rise in Morris’ tone. “I’m cool and measured.”

That may be a smug, unendearing start to an interview, but damn it, the man’s not wrong. “Everything seems amazing in retrospect,” he drawls, sounding resolutely unamazed, as Morris tries in vain to draw him into battle on such matters as the conflation of Saddam Hussein and Osama Bin Laden in the US imagination (“Oh, I don’t think so”), those confounding weapons of mass destruction (“The absence of evidence is not evidence of absence”) and the human violations of Guantanamo Bay (“Things occur that shouldn’t occur”). Most lines of enquiry are punctuated with that tightly sealed smile.

The few victories Morris claims over his subject are small ones. When Morris brings up the simple defeat he suffered to George Bush in the contest to be Ronald Reagan’s running mate, asking if he believes he missed the chance to be President, Rumsfeld’s lips purse up a little too abruptly as he concedes, “It’s possible.” For all the drastically unflattering circumstances that led to his resignation in 2006, he seems more perturbed by a loss he can’t pass off as voluntary.

And on the interview’s umpteenth reiteration of his signature knowns-and-unknowns spiel — aphoristic bosh, essentially, designed to defuse almost any given question — he finally comes unstuck, if only for a moment. Re-reading one of his famously innumerable memos, visualised throughout the film either as snowflakes or looming pillars of “Brazil”-like bureaucracy, he stumbles and admits that he may have incorrectly flipped a “known” or “unknown” here and there. It’s a small error, played for laughs, but it’s his only moment of doubt in the film, caught out as he is by his own obfuscation of the truth.

If Gibney finally scores more points over his subject than Morris does, that’s because his film at least has the advantage of multiple talking heads to fortify his stance, most of them anti-Armstrong. (I did wonder, amid the cadre of former friends and associates brought before the camera, if Armstrong’s ex-fiancee Sheryl Crow was approached for interview, given what a crucial supporting role she played, at the apex of his career, in enhancing his fairytale celebrity. I can’t imagine it was a stone left unturned.)

Morris, as is his wont, has only his subject to contend with — the more striking approach, but the more limiting one when the subject won’t be engaged. In contrast to the professionally televisual construction of “The Armstrong Lie,” “The Unknown Known” shakes out its maker’s trademark bag of formal techniques and technical embellishments, including an overegged score from Danny Elfman that plays on two definitions of horror, in an apparent attempt to make the interview content seem more dramatic by association. Morris has a more artistic filmmaking sensibility than Gibney — there’s a reason his film is in Competition at Venice, and Gibney’s isn’t. But he can also be awfully literal-minded in his choice of imagery, as when the phrase “a black hole of words” is accompanied by a digital graphic of words swirling in a vortex.

For their respective shortcomings, however, the chief reward of both films — I was about to type “pleasure,” before rethinking — is watching their subjects in repose. If there can be such a thing as defiant defeat, Lance Armstrong appears to have nailed it. Twitchy and hunted-looking as he fields Gibney’s questions without affect, he’s a different man from the guy who once brazenly rebuffed all enquiries about his drug-taking with such hypocritical self-righteousness, but his self-image is still undented: he still believes he’s the best, and did what he needed to do to prove that.

Rumsfeld, meanwhile, seems not to have changed a whit from his time in the hot seat  His unflappability is as compelling as it is enervating, perhaps because it’s a comfortable side effect of the limits of his consciousness. (Or, indeed, conscience.) Has Errol Morris failed to illuminate Donald Rumsfeld, or is there simply nothing in the shadows? Lance Armstrong could probably have taken a leaf from Rumsfeld’s book. Gibney’s cleverly selected archive footage reveals that his tack has always been so defensive, it’s a wonder he lived his lie for as long as he did. As one of these guys said — though it could have been either — everything seems amazing in retrospect.