ED-E and Boone are definitely very strong in open outside areas, ED-E is not too hampered in enclosed areas, but Boone definitely looses his edge in indoor places.

Cass is pretty much useless at long range in open areas since she's doesn't move up close to her enemies, but shoots them from afar, and since she fields a shotgun her shots miss or are ineffective 90% of the time because of large spread. Inside however, Cass is able to get right in the face of her enemy and is much much more effective.

The same can mostly be said for Lily and Veronica, their strong suit is melee, Veronica especially. Lily does have a quite strong assault carbine for long range so her skill in open areas isn't too horrible.

I haven't had Raul as a companion yet so I can't comment on him.

Rex is just immensely good, his strong suit is definitely melee since it's really the only thing he can do, but he can tank tough opponents like deathclaws and giant radscorpions for several hits, and he's very fast and unlike Cass he runs up to his opponent and delays their movement towards you the player as well as minimizing the time he is hit while not attacking anything. Because of this in my oppinion Rex is really the strongest melee companion, even though Veronica and Lily have much more deadly actual attacks.