Take note I am not a historian or very smart so take what I say with a grain of salt and understand my knowledge gaps. I would say Lincoln was Julius Caesar. A ruthless dictator who was successful in a Civil War, built infrastructure, expandanded their nation, unified their nation, and lastly was assassinated.
As for FDR, I am not sure. A man who became very ill when he was a young adult (contrary to popular belief, FDR did not have polio) and who waged war to squelch nationalist resistance in far away lands,created unsustainable welfare-state, and ruled much longer than his predecessors.
Under Tiberius and Dwight D. Eisenhower, the idea of empire took permanent root: Tiberius, like Ike was an older man and an highly successful respected general who had won brilliant victories in Germany. He was careful to rule with public dignity and decorum too and carefully saved money. The empire became more prosperous than ever.
Caligula is often comparable to Nixon but I think that is an unfair comparison. Nixon gets a unfair rap. Bill Clinton has the sexual appetite of Caligula but not sure about other facts.
Ronald Reagan is obviously Trajan who was popular among the people, he revived the Empire after the disastrous reign of Domitian(Carter).
GW Bush would be Maximinus Thrax because of his intended to make the people love him by conquest and expansion. His first campaign was against the Alamanni people of Germania. They were absolutely no threat to Rome at this time, but Maximinus invaded them and conquered them, albeit at a terrible cost to his army. The people did not love him for this, but hated him.
Not sure who is Trump, the guy who promised the people a bright future but ended up being bland and boring(BRW I voted Trump and is the furthest thing from a neocon or a progressive)
Maybe Nero is Obama but not sure