The historian Garry Wills has usefully outlined the comparisons and contrasts between Lincoln and Obama. There is the external parallel, both hailing from exotic backgrounds (Obama, of course, with the Kenya-Hawaii-Indonesia connections, and Lincoln coming from abject poverty in backwoods Kentucky, exotic in its own way) and adopting the state of Illinois as adults. Both saw themselves as outsiders until, perhaps somewhat to their own surprise, they "made it" in the ultimate political fashion.
But Wills argues that the deeper similarity is temperamental and interpersonal. They have had in common a quietly high intelligence that is deliberately downplayed, not out of any lack of ambition or confidence, but out of discretion and political astuteness. This led both to be underestimated, arguably to their benefit. The main difference between them, in terms of personality, appears to be Obama's narrower emotional range, lacking both Lincoln's disposition to melancholy and his perhaps compensatory storytelling hilarity. Obama is capable of wry humor, but he is no comedian. If anecdotal history is accurate, Lincoln may be one of the few Presidents who, were he brought back today, might be able to give Letterman, Stewart, et al a real run for their money.