That really depends on your definition of "holds up".
For example, to me the original Final Fantasy VII is still a better game than the remake because what was a well thought out RPG combat system got turned into just another button mashing combat experience with a Final Fantasy VII wallpaper applied to it.
Is the remake better graphically? sure. Does that matter to you? Than yeah...the original isn't going to hold up for you. But if you prefer the classic design from those times, the game holds up great from a gameplay/story/character perspective. And I personally would take it over whatever mash-fest modern games use for combat systems.
That game shaped my gaming life in a thousand ways. It still stands as one of my most memorable experiences.
I don't know if the emulation is the problem or not, but I've tried replaying it on multiple Genesis Emulators and found it almost impossible due to something imperceptible that makes firing the gun just a millisecond too late after pushing the button. And the group you're fighting moving just slightly faster than you. Combining to result in very quickly getting beaten to death in your very first encounter with gangers.
I've tried multiple settings on multiple emulators and I can't solve it.