I'm more interested in the Companion Perks they offer, how they benefit the game.
Check http://fallout.wikia.com/wiki/Fallout:_New_Vegas_companions , select one of the companions and check the Perks they offer when grouped with.
The one from Rex (usable items are marked when zooming; i assume containers, doors, safes, corpes, random items like notes and other use/loot-related stuff), the ED-E one (better enemy spotting + target stealthers in V.A.T.S.), the one from Boone (Highlights targeted enemies, assuming in non-V.A.T.S.) and the one from Raul (slower equipment decay rate) all look rather nice.