IMHO, it depends on the game and the remake. The old Halo games are probably the best case study on what to do and what not to do.
Halo CE - Don’t do that. The game was old enough to warrant major texture, geometry, and animation upgrades, but the developer also completely changed the art style.
Halo 2 - Do this. It’s the old art style, but with more detail. The game looks like how you think it looked, until you toggle the old graphics on and see how it ACTUALLY looked.
Halo 3 - Do this. The game was in good enough shape to just need a few frame rate, texture, and resolution bumps. New animation and geometry wasn’t needed, and avoiding that was the right call.