The difficulty balancing, hit detection and character movesets are immensely better in the SNES port. Obviously in an ideal world we'd have kept the graphical fidelity and 4 players of the Arcade game, but if you have to pick a version to play, this one far surpasses its Arcade counterpart. There's a reason everyone was disappointed when Re-Shelled came out and it was based on the Arcade version.

Thats fair

@Sprite Loving Mimiga I'm quite the opposite. The limitations prevented the animations to be smoother, the extra level is a watered down version of the first arcade game's Technodrome level, with a boss that forces you to keep tossing Foot Soldiers into the screen (Made worse on harder difficulties because the red Tonfa foot Soliders now block attacks) And Konami had a bad habit of forcing players to play the game on harder difficulties if you wanted the proper ending.
And IMO, the music took a downgrade in this port. The arcade version had multiple instruments, and the boss theme in this one sounds worse in comparison.
(The similar Genesis game, Hyperstone Heist's music was much closer to the arcade version of Turtles in Time's music, and sounds better to boot)
Another thing is the levels are missing details that were only in the arcade version. (Parallax scrolling, intro and outro for the pirate ship and locomotive, and other little details in the levels, like the circus props on the train and the domed city background in the Starbase level)

A rare case where the home port is better than the arcade version since not only does it retain the look and feel from the arcade version and the music is still fantastic, but it adds more levels and bosses including Bebop and Rocksteady. The only boss missing is Cement man and that's because he got replaced with a better boss imo.