The second game is really good. I think it's a lot funnier than the first and has more colourful areas and dialogue (although some puzzles are ridiculous).
I also see Monkey 2 as by far the superior game. The first is excellent and charming, but the second is a great work of literature. (I played Monkey 2 first though, so I'm inherently biased.)
Well, I played the first one first, and I liked that one better. Especially once you get to Monkey Island, it's one gag after the other: the three-headed monkey, the head of the navigator (which you trade in for a leaflet called "how to get ahead in navigating"), ShishKeBob and his pals ShishKeJoe and ShishKeLarry, ...
