I really cannot agree with the statement that "emulators don't feel he same as the cartridges", I think they feel pretty much exactly the same as long as I am using a real controller and ignore any emulator features (State-saves, cheat codes etc).

Also, I have yet to notice any big differences between the ROM versions and the cartridge versions.
I can even play in sync with YouTube videos of cartridge versions (yes, I have tried that), and I can keep the exactly same pace and they seem to have the exactly same colour palettes etc etc etc (I even experience the same random glitches, like for example the disappearing boss on the stage "Rat Race" in BattleToads).
There are certainly no obvious differences, let's just put it that way - I highly doubt that annyone would be able to tell the difference between a cartridge version and its respective ROM version if they didn't get any obvious clues.