I grew up in Colorado, and my mother grew up in Wyoming, so I spent summers there as a child. I currently live in Denver. Wyoming is definitely more of a cowboy culture than Colorado, and it is very rural. I drove to ND with a friend of mine last year and we didn't have cell phone reception through most of WY.
Property is definitely going to be cheaper in WY, unless you go for a rural area in CO. It will be a lot easier to find good school, doctors, jobs, etc. in Colorado simply because the population is bigger, but it is also more expensive.
While our home prices deflated significantly in the past few years, our foreclosure and unemployment rates, while high, aren't super crazy destructive high. The economy in CO tends to get hit early in recessions, but the hits aren't as hard, and don't last as long.
Wyoming also is colder and windier than CO.
Best thing I can say for Wyoming is they do have some epic outdoorsy stuff, and you can buy all the fireworks you want. I would never want to live anywhere but CO.