Vegas Cup can be a fun team bonding experience for both the kids and parents. The competition is also often good (assuming your team is placed in an appropriate flight which can be a bit of a crap shoot depending on the team) as good teams from quality programs in other states will often travel there. Stay and Play rules help with this as all the parents and kids are usually in the same hotel.
State Cup is less about team bonding and more about seeing how far the team can get in the tournament, and see where a team stacks up against other teams in the region. Since it's not stay and play parents often book different hotels for travel or just drive and go home depending on the location. There can be more games though if a team gets through the group stage and beyond so it's more soccer and can be more fun for that reason. The competition can be more variable than Vegas, particularly in the early stages for obvious reasons, but heats up in later matches as the stronger teams climb the bracket ladder.
I'm fairly sure most teams will elect for State Cup. It's an annual event in club soccer and there's an underlying expectation that every team participates in it. I can't imagine there will be any teams in the younger ages where it conflicts with Vegas Cup will elect Vegas over State Cup, but there may be a few here and there.