If you want a role playing, open-world counterpart, then shooters in general aren't what you're looking for. As I said, I don't own FC4, but from the looks of some videos, online "PVP" is just the usual run'n'gun; you do gain money although, so I assume it works counterstrike-like, as in you start with a default weapon set, kill people or play the objective to earn money and buy weapons with that money. All those activities are match-limited tho, meaning you'll start again with a basic weapon loadout in a new match and meaning nothing will carry over to single player.
Probably the only game that would fit in and meet your expectations in this case would be Firefall, a free to play MMO shooter which can be played either as a Third Person or as a First Person Shooter. It balances shooting and role-playing neatly enough, and should also have an old fashioned PVP mode.
That, or you should wait for/buy space sims such as Elite: Dangerous, Star Citizen or No Man's Sky, although they're not exactly full fledged shooters...