Man, I think I've spent way too much time down the rabit hole on this, ha. The big thing for me is how they handle the control aspect. A classic werewolf is usually a curse, right? Think Lon Chaney or 'The Wolf Man'. It's a tragic figure, forced to transform by the full moon, with zero say in the matter. The horror comes from the loss of self. Lycanthropes, in the way I see the term used more in modern fantasy and RPGs like 'Dungeons & Dragons', are often a species or a natural shape-shifter. They can change at will, they're part of a society, and they have control. It's more about culture versus curse.
There's also the look. Werewolves are often these hulking bipedal wolf-men, caught between forms, which is super creepy. Lycanthropes lean more towards a full quadruped wolf transformation, something more 'pure'. I find it interesting how urban fantasy and romance novels have totally blurred the lines though. A lot of 'werewolf' pack books now have them changing at will and having complex social structures, which is basically the lycanthrope model. So maybe the real difference now is just the vibe of the story—horror vs. fantasy adventure or romance.
Either way, I'm always here for a good transformation scene, the sound of bones cracking never gets old.