As no one has first class that flies this nonstop, you will have some combination of aircraft, so it is really hard to speak in generalities. If you post complete routings, saying what segments are available with what aircraft, folks might be able to help.

In general, you'd want to avoid regional jets for the longer part of your journey, as their First Class will be hardly worth spending the money- though it might get you to Vegas faster.


Keep in mind that equipment swaps are common, though, so no one can guarantee what plane you'll be on when you fly.
None of the airlines operate the routes you'd fly with their best first class setup. Likely, any difference will be marginal -- particularly if your concern is with the seat itself. Take a look at Seatguru.com. For example, on an A319, the following dimensions for seat and pitch on the four major carriers show no major differences:
Delta 36" pitch, 21" width
United 38", 20.5"
US Airways 37", 21"
American 38", 21"

On different planes, they could easily be swapped.