Jak II makes a lot of noticeable changes, yet it plays best when it most resembles Jak I
A recurring issue with Jak II is that the city the game takes place in is a pain in the ass to traverse. The routes are twisted and time consuming, the hovercrafts are clunky and prone to exploding, and you tend to be two steps away from pissing off a guard. Once you get to a meeting spot to engage a mission, you're greeted by angry characters caught in a three sided power struggle. The story is at it's most enjoyable when Jak & Daxter are with their familiar friends from the original game.
Missions take place in various levels. Like the story, the gameplay's strongest moments reside in familiar territory. When the game introduces adventure platforming sequences with the occasional gun combat as an extra layer, it shines. When it rides more heavily on that weapon combat or dumb side missions like racing, it doesn't fare as well. It doesn't help that the checkpoints are scarce and big chunks of progress are easy to lose.
Jak II has a lot of good game design caught in a rough new direction. It's cool that Naughty Dog evolved Jak with proven inspirations, but there have been some hitches in the process.