I didn't play the original game, but out of the characters that seem to be cut...
It seems weird that the development team is consistently only using two Ninja Turtles instead of all four. I kind of get why (it might run the risk of becoming the Nick All Star Brawl version of Fire Emblem if they go with all four Turtles, April, and Shredder), but it seems like such a bizarre move to cut two of them and add the two who weren't in the last game.
I kind of get Shredder's exclusion for wanting to avoid overdoing it with TMNT characters, but when the game is focusing on villains, it seems odd to cut one of the few playable villains from the previous game.
I'm not sure who else is being cut, but the apparent absence of Toph and CatDog seems like a shame, and it's a pity that Hugh seems to be cut when he was one of the more entertaining characters and there seemed to be a decent-sized fan campaign to include him, which even involved his original voice actor.
That's six so far - I think the other five are Oblina, Helga, Lincoln Loud, Powdered Toast Man, and Sandy, though with Sandy, I could see them wanting to avoid overdoing it with Spongebob characters similarly to the Ninja Turtles. Not familiar with the series that Lincoln Loud and Oblina are from, though I get that Ah! Real Monsters has historical importance to Nickelodeon. Not sure why Powdered Toast Man would be cut (I've only ever seen a small amount of Ren & Stimpy), but I assume he's pretty minor within the context of Ren & Stimpy, which could make a difference.
Still, I might pick up the game regardless; it seems more polished than the original, and with the possible exception of Toph, none of these are deal-breakers to me. (though it's a shame if we don't get Super Shredder in any form; it feels like an obvious pick for Shredder's super move)