It was a perfectly New York moment. I was standing on the sidewalk in front of a bar when a stranger came out on the fire escape and shouted down, “We got bin Laden!”

I brought the news into the bar, which went wild. For people in that part of lower Manhattan, 9/11 was not only a national tragedy but an assault on the neighborhood as well. Everyone remembered the hideous stench that emanated from Ground Zero for weeks.

President Barack Obama not only revealed the long arm of the U.S. law but proved that a single stunning act could transform political perceptions. From the fire escape to the bar and across the country, Obama was transformed from Professor Nice Guy into President Badass — or, rather, a winning combination of both. What seemed to be an overly affable persona turned out to be calm, cool and collected while planning a global act of precision vengeance.

Unlike former U.S. President George W. Bush, who was all strut and bluster, Sheriff Obama got his man. In another gesture of largesse, Obama invited Bush to stand with him at Ground Zero with some of the victims’ family and friends to mark the redress of that disastrous day. But Bush, who undoubtedly was worried that his own failures and puny stature would be shown up in that company, refused the invitation.

There could be two lessons for President Dmitry Medvedev in the killing of Osama bin Laden. One is that great acts of justice have the power to amaze and inspire. Russia has no cause as great as the hunt for bin Laden because its own most wanted terrorist, Shamil Basayev — the mastermind of Moscow’s Dubrovka Theater hostage incident and the takeover of the school in Beslan — was himself killed in 2006 on then-President Vladimir Putin’s watch.

Acts of derring-do always captivate the public imagination, but there are other sorts of acts of moral sweep and courage. Think of Soviet leader Nikita Khrushchev’s secret speech in 1956 or his ending of Stalin’s gulag. Both were heroic acts of justice ranging from holding the guilty accountable to freeing the wrongly accused.

The second lesson for Medvedev is that he should indeed model himself on Obama — although now, post-bin Laden, Medvedev must do it in a somewhat different way. It was always foolish and useless for Medvedev to even try to match Putin in the bare-chested, motorcycle-riding and tiger-tranquilizing department. If Medvedev is serious about being a presidential candidate in 2012 and is not just waiting for permission to run, if he has any passionate conviction about the progressive ideas he’s been espousing, he needs to do what Obama has just done: prove that he can act boldly by dispensing justice. Pardoning former Yukos CEO Mikhail Khodorkovsky is one example that comes to mind.

But it looks like Medvedev has chosen other models. As The Moscow Times reported on Friday, “Medvedev at the last minute dodged a meeting with mothers who lost their children in the bloody Beslan crisis, possibly fearing that they would criticize his patron and predecessor.”

You can dispute Medvedev’s motives for this act, but the failure to face the Beslan mothers can hardly be termed strong, courageous or presidential. As bad luck would have it, Medvedev is imitating the wrong U.S. president: the stunted Bush, not the grand Obama.