Is it better to liberate an outpost by going stealth or loud?
You get bonus XP if you do it undetected, the game will tell you with a notification at the top-left. Undetected as in enemies never see you, you can blow them up to kingdom come with the loudest explosives this side of Himalaya and as long as they don't see you you're still okay.
Also, liberating 2 outposts undetected is required to unlock Soft Landing, which is required to unlock Non Stop (unlimited sprinting)