I’m generally trying to keep two scenarios apart, one is bossing or raiding and the other is mobbing. In mobbing, no character is better and more useful to a team than Maya, everyone already said that. If we move on to raiding (and I consider the raid on digistruct peak to be a “raid”, just not in the classical borderlands way of raiding), a lot more opportunities for other characters open up. For example, @BookEmDano’s point about Salvador providing bullets for the team can actually be seen as a real plus for him. In general mobbing, ammo spews out from everywhere and if you run low on ammo on any character, a bullet regeneration of 1.5 won’t change much for you as your team will pick up ammo from other places faster than this could take any “real” effect. Of course, DPS is his domain and he does it exceptionally good.
Again, for Zer0, B0re is good and all, but isn’t a deciding factor when mobbing. It can make bullets count double or triple on a few occasions and when paired with a Maya and Converge these occasions multiply, but again, Maya is good with anyone. When it comes to b0re-able enemies, nothing kills the boss (and the fun for others :p) faster than him. I’d choose a Zer0 over a Maya against Hyperius almost any time.
There are always some exceptions. Like how Axton’s turret’s shield can absorb some raid bosses’ attack (I don’t remember which one), or how hellborn Krieg is a strain for the eyes but needs little to no help either. Every character can help a little in one way or another, even Gaige and her aggro-drawing pet. I have no particular “favourite” character, I play every character equally… except for Gaige, I just can’t seem to understand how she works. I cannot remember each and every use for each character either, pure zer0-players will always know more about him than I do, for example. Also, a lot of a character’s viability depends on the player himself. I’ve even seen salvadors respawning