I've worked for both. I had better benefits when I was with the State (e.g. free health insurance) but, in most cases, Federal pay is better. Of course, I left State gov't in the mid-90s so the benefits thing may have changed since then. I also know more state employees who have had to deal with RIFS/furloughs than I do Feds who have endured the same. IMO, Federal positions are more secure (although some agencies are more vulnerable than others).
With that said, there's wide variation across states in terms of how they compensate their employees, so it's difficult to generalize. It's pretty much a lock that you would earn more in MD, for example, than in states like WV, MS or NM.