Spidey, I think it's like a saying that they toss around in sports: You don't want to be the guy that follows a legend. You want to be the guy who follows the guy who follows the legend.
Allow me to present my take on the perceived difference.
B:TAS (and by extension, the entire DCAU) was so well-received and acclaimed and rich in its portrayals, that the next animated series to focus on Batman was likely to be the recipient of heightened scrutiny. Even though B:TAS ended in '97 (or '95 if you want to separate
Gotham Knights, which received its own criticism for 'not being B:TAS enough'), there was still plenty of that 'universe's' Batman that could be seen in syndication, as well as through
Justice League/Justice League Unlimited, which was still on the air when
The Batman premiered in 2004. Having such a thorough and favored character interpretation still active while a new show came on was going to rankle some people and bring the immediate question 'Why don't they just continue B:TAS?' There was an identifiable overlap in proximity. Comparison and inevitable disdain could almost be guaranteed as a reaction within the fanbase ...and that's even before one episode of
The Batman was broadcast.
Another reason why
The Batman caught so much flak was due to its aesthetics. It's art style came off as some anime-inspired acid trip and a number of the 'new' character designs struck me as ridiculous. A little revamp isn't necessarily a bad thing, but some of those choices were just awful (Joker, Penguin and Bane, to start off with).
Lastly, I found the show (save Season 4) rather bland throughout its duration. The lighter' tone of the stories wasn't really a problem. However, the execution of the episodes and subject matter left a little to be desired. Outside of the mentioned exclusion, it just wasn't that good on a consistent basis. That surely did it no favors.
Batman: The Brave and the Bold, while not completely immune to the above criticisms, doesn't suffer from them in the same regard. Though the B:TAS incarnation is still fondly remembered, some time has passed since it ended, including the passage of another show that's taken some of the sting off. The character designs (and implied tone) don't seem that drastic. They strike me as a slightly modified interpretation of the Silver Age. There's a familiarity there, that speaks against trying to re-invent the wheel. Also, I believe it holds some appeal as it's reflective of the style of Batman which was introduced a number of us to the character; be it the actual books, the old '60's show or the varied SuperFriends iterations. Overall, the show just looks fun. It's not trying to be the dark and brooding Batman, but seems to be going for a different entertainment quotient that won't relegate it to being silly, but will explore a little levity mixed alongside the heroism that we expect from Batman. Ultimately, the show will be judged on how good it is. Even though we've yet to see exactly what that is, for a number of the reasons listed above, I can see how people would be more receptive to this than the last animated Batman offering.
...or something like that.