Diablo

I haven't played it yet, but from what I've gathered, DevilutionX is basically about reverse engineering the original Diablo 1 code for preservation purposes - to the point that you can even compile it with the ancient Visual C++ 6 compiler, plus bringing in some much-needed modern QoL changes in moderate doses, to stay true to the original.

Belzebub on the other hand aims to bring in more of a content and gameplay changes, such as adding new classes (Barbarian, Assassin), new monsters, items, spells/skills etc (most of this is taken from D2). From what I've seen and heard though, this has been done really well and for many, this is the mod to play - especially if you're coming from D2 and miss some of the stuff in it. However, if you're after a mostly authentic experience then DevilutionX is the way to go.

Most notably though, Belzebub is single-player only, unlike DevilutionX which now supports multiplayer. For multiplayer, the guys behind Belzebub made a continuation of the mod called Tchernobog, which adds multiplayer (but sadly, you can't do any quests if you're playing multiplayer). Looking at the changes, Tchernobog seems even more comprehensive than Belzebub was, as it even added another class from D2, the Necromancer.

In summary, from reading the changes, I think Belzebub and Tchernobog are the mods to play if you're after a fun experience, but DevilutionX is the one to play if you're after an authentic experience.