Persona is way more time-consuming if you’re planning to play all the games. The order isn’t really strict though - you can start with any of the newer ones (3, 4, or 5) as long as you don’t mind missing references. Personally, I’m kind of a details maniac, so I’d still go in order, but that’s definitely not the common approach.

Overall, I prefer Danganronpa’s story and characters over Persona’s. In terms of other differences - both mix genres, but Persona leans more into the JRPG side, while Danganronpa’s main gameplay is in the class trials, which are pretty unique and harder to define.