A B/B pet always has 2 higher stats than its purebreed counterparts (H/H, P/P, S/S) so B/B is not a bad breed, it's just the one with the fewest total points to share. I have a few B/B's that I prefer over some other breeds of those particular pets because the B/B makes more sense with that pet's moveset. Then again maybe that extra little power isn't enough to make you prefer it over an H/S breed for example. Usually if it's a pet with B/B or P/B as the only choices I'll go with the P/B because that extra little power makes me feel a little more secure. But the B/B will be faster than the P/B. So it all really comes down to what you prefer as a stat.
One pet I recommend getting in B/B is the Crystal Spider. And if you fight with any of the B/Bs in your collection and you're just not happy with it, try a different breed. For the most part I'm not too picky, because all the cats have the same moves as do the rats/snakes/roaches... there's no point in getting rid of a rare B/B if you already have other rats/snakes/roaches who all do the same stuff. I have an S/S roach and a P/S roach, all the other roaches I didn't care as long as it was rare