I'm actually going to remove my Nostalgia Goggles and my blinding bias and say that The Spectacular Spider-Man is the better show. Why?
Due to some meddling with a former editor, B:TAS was stuck with some truly bad episodes that were meant to pander to the younger viewers. For every "Two-Face" or "Heart of Ice", there was "I've Got Batman in my Basement" or "Cat Scratch Fever". Characterization was also inconsistent. Characters with impressive first showings like Two-Face and Clayface were reduced to common crooks with gimmicks over time, and Killer Croc kept being flip-flopped between being a cunning adversary and an idiot. And while the designs were stylized to allow better animation, it still came up looking sloppy in some episodes.
Contrast that with SSM, which had more consistent quality in episodes, better characterization and development for both major and minor characters, and though having even more simplified designs, had smooth animation all the way through.
And the whole quantity=quality argument that some of you are having is completely unfair. It's not SSM's fault that it got screwed over by company politics. Warner Brothers is just far more competent and faithful to its properties and employees, and allowed B:TAS to flourish and develop. If B:TAS was shortened by 26 episodes, would you guys still consider it the superior show?
It sounds like I hate B:TAS. I do not. It was, and still is, a critical part of my childhood, and it is a show that played a major role in revamping the animation industry in the 90's. But the show itself, as influential as it is, is far from perfect, and it has several flaws that would not allow it to last today's standards. SSM is just the strongest show to me.