Happily, figuring this out is just numbers. So here are the most successful Democratic and Republican state parties since 2004, in terms of percentage of wins in those elections.
The winningest Democratic states won more regularly than the winningest Republican states, but that lead fades quickly. Overall, more states had more Republican wins (31) than Democratic ones (19). The closest to the middle is Wisconsin, which has slightly preferred Republicans.
This is not as neatly structured as you might think. Even some of the most Republican states have voted more heavily for Democrats in some years. Here's the overall percentage and number of net wins for each state, plus the percentage of victory for each party in each election since 2004.
Comparing 2010 and 2008 is instructive. In the former, more states saw Republicans with net victories. In the election of Barack Obama, though, more states leaned more heavily Democratic. Note, too, the big difference in actual net wins. California may not be the most reliably Democratic state, but it has elected far more Democrats than any other.
Anyway, congratulations to whoever runs the Democratic party in Massachusetts and the Republican chairman in Idaho. You've had quite a decade. Not, we suspect, that you had to do all that much to make that happen.