I've only just started season 2 of Spectacular Spider-Man (and have seen all of TAS and am currently re-watching it) but here are my thoughts:
Spectacular's action and animation was a huge improvement on TAS and I admire the simplicity of the art style. However, it felt like it tried to do too much, story arcs occurring way too quickly. To clarify, it didn't feel like they were just cramming things in for the sake of it, but, for example, we got the S6 so soon and Venom felt rushed and forced for the finale; Eddie's hatred for Peter was too sudden towards the end of season 1 and I think it would have been best if they covered Eddie over the two seasons. (no spoilers please, I don't know if Venom makes a re-appearance after season 1 just yet)
Spider-Man: TAS did a great job of fleshing out story arcs and many characters for their appearances to be meaningful and memorable and their roles having significance in the story. While the recycling of animation and Spidey's poor combat skills were a letdown for the show, the series still carried a lot of heart and featured great storytelling. It was nice to see Peter's/Spider-Man's intelligence come to good use too, showing that he's capable of more than just swinging around the city and kicking a thug or two.
It's taken a while for Spectacular to grow on me and I think the best thing about the show is the focus made on Peter's own life which I actually enjoy watching more than the Spider-Man moments. I like how troubled Peter is yet he still tries to look out for his friends and Aunt May and does his best at balancing his dual-identities. While TAS took Peter's circle of friends and spread them out over several seasons, focusing on one or two characters and then leaving the majority absent, I've liked how we've immediately gotten to see Peter interacting with everyone at high school and I like how they keep toying with Peter's romance with 3 potential love interests at the ready for him (Liz, Gwen, MJ) yet it takes Peter a while to decide who he really has feelings for and he's still quite awkward around the ladies, despite their obvious interest in him. From what I recall in TAS, Peter's more likely to be called up on a date and doesn't seem to have much of a problem with women, it's just turning up on time and not letting Spider-Man get in the way that is the problem for him. Going back to SSM, that's something that resonates really with me and I like how "human" Peter feels; his life as a teenager is believable and Peter is easily likeable, making it all the more easy to root for him.
On a little side-note, I get what they were trying to do with SM2, related to what I've mentioned above and having a Peter Parker that is struggling to balance his life as a student and as Spider-Man, but Spectacular handles that a lot better; Tobey Maguire's lack of charisma and almost lifeless performance as Peter in that film is one of the main things that turns me off what everyone calls the greatest Spider-Man movie ever. If Maguire had retained that energy he had from SM1, then yeah, maybe I would have felt a lot more for him in SM2 but he was just too boring and miserable. If they'd characterised Peter in SM2 similar to Peter in SSM then I wouldn't have anything to critique about the second installment in the trilogy.
I know this thread isn't dedicated specifically to whether TAS or SSM is better but I know that the two shows have sat very well with fans, hence the comparisons made between the two.
Spider-Man: The Animated Series gets a score of 8.5/10 from me, I love that show and wouldn't get bored of watching it over and over again. Christopher Daniel Barnes is great and his performance will never be forgotten. The cameos from other Marvel characters, incorporated into the storyline, has always been fun to watch and if it hadn't had been for TAS, I would never have had heard about a lot of these other Marvel characters as a kid, being completely new to their introduction now (in the MCU and other media). Spectacular Spider-Man has some great elements but IMO it suffers from Spider-Man's encounter with villains and tackling crime being a little too condensed.