I've actually never played the second one.
I actually choose Jazz Jack Rabbit as my new "favorite game" to match my new "favorite movie" by looking up a list of games from 1994 and choosing the worst one I could remember playing that didn't have Star Wars in its title. Not that I didn't enjoy Jazz Jack Rabbit, I only ever had the demo version, but I have no doubt it ranks as the demo I have by far spent the most time on in my entire life.
The demo threw constant subliminal and non-subliminal advertisements for the Gravis gamepad at players and that always made me really want one. One day I found one on clearance and an Electronics Boutique and thanks to Jazz Jack Rabbit I didn't even have to think twice about blowing $10 on the thing. I went home in a mild state of euphoria, feeling kind of like I just found my own personal Holy Grail. I'm telling you, if that wasn't one of the biggest wastes of $10 I ever spent in my entire life...