I first saw Steven Spielberg's biopic of America's most popular president in a packed cinema in New York's Lincoln Square.

You could have heard a pin drop. That the audience was there, in the first place, says much about the country's current willingness to engage with serious films that touch on sensitive moments in its past; that they were so rapt before Lincoln is testimony to its powerful hold.

As a biopic, Tony Kushner's intelligent, fascinating screen- play is particularly well conceived, for it focuses on just one month in the president's life, yet reveals through that narrow window his entire biography and the essence of his character.

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That month is January 1865. The civil war is almost won, but Lincoln (Daniel Day-Lewis) is far from content. He knows that victory will not be enough to defeat slavery, that abolition needs to be enshrined in law; but if the war is won first, Congress will feel no need or desire to pass such a law. And so he embarks on an intense period of lobbying – using compromise, manoeuvre and skulduggery – to unite the House of Representatives behind his 13th amendment.

Spielberg offers a couple of gory glimpses of the battlefield to remind us of the terrible cost of the war and the moral problem with Lincoln's tactics, which involved delaying a peace treaty until the amendment was passed. But most of this dialogue-dominated film takes place in the drawing rooms and debating chambers of Washington. Here, in another remarkable performance, Day-Lewis's Lincoln is physically weighed down by melancholy, the pain of the crisis etched deeply into his face; but he can also be charming and funny and fiercely determined. The idealism and humanity are so palpable, we are left in no doubt why this president was and is revered.

While Day-Lewis offers the captivating presence at the heart of the film, he's surrounded by a corking cast that includes James Spader as a roguish lobbyist, David Strathairn as secretary of state William H Seward and Tommy Lee Jones as the radical abolitionist Thaddeus Stevens, who puts his ambitions for black equality aside in service of Lincoln's pragmatic recognition that "freedom comes first".

Kathryn Bigelow's Zero Dark Thirty is also concerned with the moral undertow of history, albeit history so fresh that it still hurts – namely the war against terror. Some American critics have condemned what they perceive as the film's endorsement of torture during the decade-long hunt for Osama Bin Laden by US intelligence officers, which ended with his death in 2011. Their objections are facile. Scripted by Mark Boal (who earlier teamed with the director on The Hurt Locker), this is neither triumphalist nor apologetic, but a steely, warts-and-all account of the dogged pursuit of a shadow.

Like Lincoln, it's a procedural, showing the different approaches used – torture being one, endless surveillance another. Also like Lincoln, it is an homage to selfless tenaciousness, in this case that of CIA operative Maya (Jessica Chastain, playing an amalgam of several female agents) who obsessively leads the search. The waterboarding scenes are certainly discomforting, in part because for Maya and her colleagues this is just another day in the office. And that has to have an effect: Chastain's intense performance reveals the sacrifices her character makes, becoming too hardened for everyday life and relationships.

It is a brilliant film, gripping and thought-provoking, which dares to raise questions without answering them and, despite our knowing the outcome, winds the tension in the auditorium to breaking point.