Studies show that, increasingly, it’s the Democrats. Class appears to be diminishing as a political divider, replaced, perhaps, by one’s attitude toward government (upper middle class civil servants aren’t exactly hostile to it) and one’s stance on moral issues. I’d like to think that the fact that Democrats have lots of wealthy supporters will mean that they’ll become sensible on economic policy, but a lot, of course, depends upon the source of the wealth (trial lawyers not being known as friends of productivity, for example).
Update: For another view, go here: as long as Democrats can be identified as the party of tax-and-spend, the wealthy have the incentive to vote their pocketbooks with the Republicans, but if taxes are essentially off the table (as they have been in recent years), the "natural" advantage Republicans have goes away. What happens if the Democrats begin to think about raising taxes again?