I like demon eyes more in terms of aesthetics, and combat.
It sort of introduces the concept of the eye type enemy in Terraria which leads into a boss version of the enemy in the form of EoC and the Twins. And they are more difficult to deal with than zombies. For zombies, you can trap them, and use the Terrain to your advantage to make them unable to reach you. But it isn't as easy to do the same with demon eyes. They are more dangerous to deal with than regular zombies.
Zombies can drop the Zombie Arm, and a shackle which make for a good early game weapon and beginning accessory, but I'm not as interested in zombies overall. Part of it could be due to the oversaturation of them in many other kinds of games/movies.
They also drop lens which allow you to craft summoners for the EoC and from there get Crimtane/Demonite Ore, Seeds, and the Shield of Cthulhu (one of the best Expert Mode accessories in my opinion)
Aside from that I'm interested in eyes in general and it feels like a pretty unique enemy to Terraria. I prefer demon eyes over zombies.