A generator can be fussy, can require fine-tuning as your electrical use patterns change. If they're not set up right, they can be hard on the battery and electrical components. Whereas an alternator is usually plug-and-play. However, if the rest of the engine bay is stock-looking, an alternator looks out of place, IMO, unless you get one of the
very expensive ones that's built to look like a generator.
The best of both worlds is a rebuilt generator with an EVR. Unfortunately, no one is making EVRs right this minute.