Graphically inferior, yet ultimately better than, the arcade game.
Hindsight being 20/20, it’s difficult to understand how the original NES TMNT game received a sequel at all - wait, no it’s not - the game was a massive commercial success. Well, thank Cthulhu that Ultra Games completely changed up the formula for the follow-up, taking inspiration from the concurrent four-player arcade cabinet that was massively popular at the time. It was simply called Teenage Mutant Ninja Turtles, a sidescrolling beat ‘em up in the spirit of X-Men and Streets of Rage. The critical difference is that it starred everybody’s favorite terrapin heroes, who were at the height of their popularity at the time.
The NES version necessarily toned down the graphical fidelity and special effects. Everything looks completely different but is still clearly inspired by the arcade game. The Turtles especially look significantly different, as do most of the bosses. Happily, the music is largely on-par with the arcade version. Another disappointing, but unavoidable, downgrade was the disappearance of four-player co-op, replaced instead by two-player co-op, which was still incredibly fun and, I would assert, the only way to play the game. Despite its technical downgrades, TMNT 2 is still one of the best co-op experiences on the NES.
While the NES version may not look as pretty as its arcade counterpart, it does feature some awesome exclusive content that enhances and lengthens the game considerably. The NES game has two original levels that are absent from the arcade version that end with two new bosses. In the first original level, the turtles trek through a snow-covered Central Park that has been under assault by Shredder’s weather machine (seen in the 1980’s cartoon) and at the end of the stage, they battle a silly-looking wolf boss, Tora, who wears a leather jacket. The second level takes place in a Japanese-inspired building where the Turtles end up fighting a robotic (and very difficult) Shogun.
Many other stages were changed or extended as well. Notably, in the arcade version at the end of the third level, you battle Bebop and Rocksteady. In the NES game, the third level is lengthened considerably and the Turtles face Baxter Stockman instead.
The NES game also features one of the cooler Shredder fights in the series: he duplicates himself, and the only way to tell which one is the real Shredder is to knock one of their helmets off - that one is the fake Shredder, so go after the helmeted one! After a while, his helmet will be knocked off, too, and he’ll be unable to clone himself anymore. It’s a great fight that’s pretty tense (he has a one-hit-kill ray) and you feel great when you beat him. Of course, the best way to beat him - and every other enemy in the game - is to spam the jump-kick attack. My brother and I eventually got the timing exactly right so we were almost never hit by enemies: jump forward, kick, jump away, kick back toward, repeat ad nauseum. It was very effective.
It’s probably not too difficult to track down a copy of the NES cart, but the arcade original is on XBLA for pretty cheap and it does have four-player co-op. Me? I’d try and get both... and a working NES. The game is available on a wealth of systems: PC DOS, the Amiga, the freaking Commodore 64, and the Amstrad. So you've got options!