Power Map: State Governments
In a handful of states, the party in control of the legislature has enough votes to override the veto of the governor of the opposing party. Democrats have override power in (6): Arkansas, Maryland, Hawaii, Massachusetts, Rhode Island, and Connecticut. Republicans have override power in Wyoming, and are just shy in Kansas.
States where a Republican legislature is checked only by the threat of a veto from a Democratic governor include (6): Michigan, Wisconsin, Pennsylvania, New Hampshire, Virginia, and Arizona. States where a Democratic legislature is checked only by the threat of a veto from a Republican governor are (5): California, Colorado, Alabama, Mississippi, and Vermont.
States with a split legislature and a Democratic governor (6): Oregon, Montana, Iowa, Oklahoma, Delaware and Tennessee. States with a split legislature and a Republican governor (4): Nevada, Minnesota, Kentucky, and New York.
So, to illustrate this as a spectrum, control of state legislatures looks like this:
D: 8 5 6 6..4 6 2 13 :R
There are 25 states with more Republican control than Democratic. There are 25 states with more Democratic control than Republican. But among states Republicans control, they control them a little more strongly.
One additional note. Southern Democrats are very difficult for the national party to control, and far less likely to want to try any sort of partisan shenanigans in favor of the national party. This is an institutional problem the Democrats have that Republicans do not, for the most part, have any couterpart to. As such, Democratic partisan strength is overestimated by looking only at the numbers.
(Graph from Polidata)