I haven't been in all that long, but from what I've heard the Merlin Mk2 is generally more permanently active, doing longer deployments but not as often. However, the Wildcat tends to do small ship stuff more, and the small ships go out a fair bit so if you end up on the frontline squadrons for that (815 & 847) you'll go on shorter trips but more frequently.
Merlin Mk3 is not up to all that much at the moment, which is the source of a lot of grumbling on their part because the CHF engineers are getting a bit bored. Mind you, it's the same on 825 at the moment.
I can't speak for the F-35 because well, it isn't here yet. I'm sure when it does become fully integrated they'll be doing a lot of things on the QE to test it out, but only time will tell. I can't suggest anything because each person has their own interests. I chose the Wildcat because I wanted to work with the small ships aspect, and also the turret on that things is what was the driving attraction, because I wanted avionics.
The man difference is the bases I guess. RNAS Culdrose is probably the nicer base (ie, more to do there) but has little nearby. RNAS Yeovilton is the opposite. However I'd say don't choose your aircraft based on where it's located. Choose it for the job you want. That said, if I'm still at 825 and you end up there, you'll be greeted warmly.
