I say TSSM, and it's not just because I'm biased towards Spider-Man.
To explain, I've copied this post I made on TV.com in response to an argument that BTAS is more mature, emotional, and dramatic.
Mature: Yeah, Batman is, because, well, it's Batman. However, one thing which I greatly respect about TSSM is how (as Weisman) it "works in different circles". Children will enjoy it for its excitement and humor. Older audiences will love it for its character development and intensive plots. Furthermore, there are some tidbits which are targeted for a specific without diminishing the other's experience - best example being Black Cat's innuendo.
Emotional: I'd say they're about the same, actually. The level of emotion, usually, is directly related to how well-developed and relatable the characters appear, so I'm gonna argue on that note since it's easier to understand. BTAS has a lot of characters following this criteria - Mr. Freeze, Mad Hatter, Batman himself, etc. - and a bunch who don't - Clock King, Penguin, Croc, etc. - and a lot in-between - Catwoman, Harley, Bullock, etc. Mainly, BTAS' most emotional characters are based in tragedy and how it transformed them. TSSM, on the other hand, also has a lot of emotional characters - Spider-Man, Liz, Gwen, etc. - and a bunch who don't - Sally, Shocker, Betty, etc. - and a lot in-between - JJJ, Flash, Vulture, etc. However, though it does have it's share of tragedy with guys like Molten Man and Electro, TSSM focuses a lot more of its emotion on issues that people typically face in life, like balancing school with work with friends, and having money troubles, trying to get a girl, etc. So yeah, it's different types of emotion, but the two are definitely at around the same level.
Dramatic: Again, like with the emotional, drama isn't always tragedy. The end of Natural Selection, for example, wasn't tragic - it was uplifting, even - but it was still definitely dramatic. I'd say they're at the same pace here as well (considering that dramatic is almost the same thing as emotional ).
Plus, TSSM does have several things over BTAS!
Continuity: They're two very different shows. BTAS goes with an episode-by-episode format, however TSSM develops over time. It's a lot of preference, but I prefer the continuity because it allows you to watch characters like Electro and Liz evolve over time, so that we can see long-term reactions and effects. With BTAS, there were several cases, like with Mad Hatter and Two-Face (he never really returned until Second Chance as far as I'm concerned), where great development was lost due to this lack of continuity. Sometimes, it even contradicted itself - Joker has now lead two past lives, one as a gangster (Mask of the Phantasm), and one as a comedian (his final episode - I forget the name). TSSM, on the other hand, is usually quite consistent with its characters.
Relatability: Face it - you don't really know what if feels to run around at night wearing a cape and cowl and fighting criminals. TSSM incorporates Peter Parker leading a regular life alongside his Spider-Man one, and thus retrieves a far greater level of relatability. They're two completely different heroes - opposites, in fact - Bruce Wayne has truly become Batman, while Spider-Man still maintains his Peter Parker persona as the dominant one.
Humor: It's not that big a deal, but it's still true.
Action: Again, it means barely anything, but TSSM has had way better fight scenes than BTAS.
Animation: Okay, this really means next to nothing, but I still definitely prefer TSSM's great, fluid animation to BTAS' still great, but not as great animation.
Don't get me wrong - I love BTAS a lot and it's probably my second-favorite show now, but TSSM has a lot over it, and that's not just the bias talking.
Seriously though, here's my official (objective) stance on this debate:
It all comes down to preference.
Both shows are at the same level as writing. Remember, writing is extremely subjective, and the only way to truly judge it is by well the show or movie or book or whatever accomplishes it's goal. You can't favor one format over another writing-wise because the first rule of writing is that there are no rules! As someone previously mentioned, Spider-Man just works better as a continuous series, and Batman may work better as an episodic one.
In the end, here's what it comes down to:
BTAS has a dark tone, tragedy, and an episodic format.
TSSM has a light tone, relatablity, and a continuous format.
Take your pick.
Personally, I prefer relatability and a continuous format (though I have no preference over dark/light tones), so I'm going for TSSM.
That's all there is to it.