Batman: Brave & The Bold is better than Batman: The Animated Series. Much better.
Yeah; I said it. You wanna make sumpthin out of it, buddy?
BTAS: brooding and morose, taking itself too seriously. Why, it's nearly a... a Marvel comic!
BB&B: still serious (Batman's still quite the hard-nose), but not taking itself too seriously.
BB&B has better art. I still remember how disappointed I was the first time I saw BTAS. This was before the current info-age, when I would have seen 10,000 spoiler images for 8 months beforehand, so the first time I saw it actually was the first time I saw it. How shocked I was! I was expecting to get, finally a detailed, beautifully drawn animated series that actually looked like a comic book I might already be reading. Instead, I got pointy noises and square jaws that would have embarrassed even Bob Kane.
BB&B is better promo for DC. You may not consider that an appropriate aesthetic considering, but, hey, marketing matters. BB&B is designed to use Batman as a means to introduce viewers to other DC characters. So far, we've already seen in three episodes the likes of Plastic Man, Blue Beetle, Aquaman, Fire, the Gentleman Ghost, Green Arrow, Clock King, Black Manta, Felix Faust, and Ocean Master. In BTAS, we saw... Robin and Batgirl. The opening sequence of BB&B actually builds the names of various guest stars into the layout; the opening sequence of BTAS doesn't even contain Batman's name.
BB&B is better characterization. This Batman is still a hard-nose (even harder than the BTAS one), but has a sense of humor. His scene where he mocks Felix Faust is priceless. And Batman's unique personality is shown off in excellent contradistinction against the guest stars. And Dietrich Bader is flawless as Batman, much to my surprise.
BB&B is better action. Each episode begins in medias res, and has little slow time till the end. Plus, no time is wasted on Bruce Wayne; it's all Batman. More happens in one episode then in a year's worth of JLA.
BB&B has better decor. Yep, you heard me. BTAS was clunky, with its overly long Batmobile and colorless Batcave. Every single bat-gadget in BB&B is stylish, with red accents and bat shapeyness. BTAS is a PC and BB&B is a Mac.