The Batman is the best animated Batman series ever done. Yes, better than BTAS.
Rino Romano is a better and more complete Batman voice than Kevin Conroy. Not by much, but still better. BTAS forced his brooding upon us, where as The Batman, his introspective seems more organic. There is always a reason behind it.
I prefer the older Batgirl, but I see why they did it. It allows Batgirl & Robin to play off each other, rather than relying on it always being Batman.
The best Mr Freeze origin is from this series. He is no longer a tragic figure, who really turns out creepy, which we finally see in Batman Beyond (Which takes place in the same universe as BTAS.) Freeze in The Batman is a villain hoisted in his own petard and uses his new found power as any good villain should.
We see The Penguin for what he is, a spoiled brat, that believes the world owes him riches and acceptance. He is a petty and arrogant little SOB.
We see the Joker as truly an agent of chaos and a much truer antithesis of Batman than we got in BTAS.
Finally, the batmobile is more functional and practical. Not bound to Burton’s Batman.
In the end, THAT is what makes it better than BTAS, it is not beholden to Burton’s vision of Batman & Bruce Wayne. It is original. It truly does the character justice by being an original and reasonably comic book canonical Batman.