Which stud should I mount to if they are different widths?
The 3.5" studs are either doubled-up 2x4s, or a sideways 2x4. I would use the 2" studs to mount it on because if the 3.5" studs are sideways, they will be more likely to bow out under load, and a regular 2x4 is more than strong enough to hold body weight.