I think in reality, the democrats. It seems that the GOP is more diverse with its fighting within its own circles, but the D's have a bigger coalition. All Republicans seems to have the same rhetoric, values, beliefs to me. Maybe Rick Santorum to Rand Paul is the biggest stretch you can get. But the Dems compromise groups of people from old democrats in Appalachia to staunch progressive, anti-war, anti-establishment activists in California.
There aren't many Coal Country Democrats left though, even if there are many Southern Conservatives who claim to be Democrats.
I would go with the Republicans being more diverse, at least amongst its voters in Presidential elections on social issues. How else do you get an Evangelical wave (though it was more likely that if you replaced Obamacare with Iraq, you get 2012) in 2004 where the top of ticket's voters were one third pro-choice?