I've had my beta for over 11 years now. In that time, he (or she, who knows?) has lived with two separate yellow tangs, one in a 135 and now a different tang in a 180. Both tangs stayed near the beta, or maybe it's vice versa, almost constantly. Either way, it's a rare things to see them on different sides of the aquarium. My wife jokes about their "relationship."
The beta is slow swimmer, but he's definitey not shy. In that 11 years, he has figure out where his food comes from and if I'm near the tank, he's always front and center looking for a meal. The tang is a far more aggressive eater, but every three days or so I drop in a larger piece that the tang can't easily eat. He generally gets at it first, but since he can only chew on a corner of it, the beta ends up gulping it down.
Anyways, my point is these two species have always lived very well together in my aquariums.