Misleading thread title but whatever.
I have no idea what faction gives the most exp, I don't keep count on it.
But Legion has fewer quests than NCR, and if you kill NCR and get vilified you are locked out of more quests than you earn.
Still, it's worth giving a try.
Joining Legion gives you access to unlimited free stealthboys, a centurion armor in their safehouse (which is the Legion's strongest armor, not a PA though) you get some unique weapons from them and from killing NCR, you can fight in the arena if you are male and you get free Legion gold from their dropboxes which refill every couple of days.
The drawbacks are the loss of quests really.
Camp McCarran, Camp Gold, Camp Forlorn Hope et cetera.
Other than that I can't think of many drawbacks.
As long as you don't kill Van Graffs or anything you can still use most vendors in the wasteland.
Oh and Arcade, Boone and Veronica will likely leave you at some point.
Arcade can be sold into slavery though.
And Veronica can be served to White Glove Society during that quest for the Legion.