I don't think you can use Texas due to our climate, diversity and the spread-outedness of it. There's not really a corollary for Texas anywhere in the country. Same problem with Cali and Florida. Texas vs. California doesn't really work either because we don't have any mass transit, and our population density in the cities is still much lower than Cali. I think you'd need to pick two relatively homogenous states that have similar climates and population densities.
I'd do Illinois vs. Indiana, or Michigan vs. Pennsylvania. Probably the latter, because with IL vs. IN you have one with a huge city and one without.
You definitely have to control for climate, though. I'm pretty confident the hot southern states and California are faring better right now because of the weather.
This might help:
https://www.nytimes.com/interactive/2020/us/states-reopen-map-coronavirus.html
I hope you go forward with it - always interested in this type of analysis.