First, consider the Carter/Obama comparison. Economic difficulties, some of international origin, beset both presidencies. For Carter, the rise in global oil prices sparked an energy crisis. A different sort of energy crisis, triggered by the Gulf oil spill, afflicts Obama. A sluggish international economy is proving to be an important problem for both presidencies. And both Carter and Obama made energy policy a central priority of their presidencies.
Controversy surrounded the shifts in foreign policy initiated by Obama and Carter away from the more assertive policies of their GOP predecessors. In Carter's case, his foreign policy encountered the costly crises of Iranian hostages and the Soviet invasion of Afghanistan. Obama's foreign policy faces stiff challenges -- if not yet full-blown crises -- from the rogue regimes of Iran and North Korea.
Obama and Carter have similar personalities, according to Stephen Rubenzer, a psychologist and coauthor of an important book on presidential personality (Personality, Character and Leadership in the White House (Brassey's, 2004)). He classifies both of them as "philosophes," a category they share with Lincoln and Jefferson. Philosophes tend to be high in character, neuroticism, extraversion, agreeableness and conscientiousness. Those traits contributed to successful presidencies in the nineteenth century, but did not ensure success for Carter. The accuracy of this personality analysis for Obama is not yet clear.
Now, the Reagan/Obama comparison. Like Reagan, Obama inherited major economic and foreign policy problems from his predecessor. Obama and Reagan, each manifesting a distinct ideological profile, sought to move government in their preferred ideological direction. Both sought to make their approach -- Reagan's conservatism and Obama's liberalism -- more broadly palatable to the public. Both proved to be skilled public communicators. Both accomplished big changes in government in their first year, Reagan through tax and spending cuts and Obama through his health care reform.
These traits made both Reagan and Obama polarizing figures during their early years in office. The sluggish economy reduced Reagan's job approval to the low 40s by 1982. Obama remains in the mid to high 40s as of mid 2010. The robust economic recovery of 1983-4 propelled Reagan to a landslide victory in 1984. The fate of Obama's presidency may depend on a similar economic performance.
Your view of Obama as Reagan or as Carter may depend on your approval of his conduct of the presidency. As time passes, a series of continuing policy reversals will cause the Carter resemblance to strengthen, but an economic rebound may give Obama an opportunity to dominate national politics, as did Reagan. Obama no doubt wishes for the latter fate.