Back in the older Crash games, we were limited to having the camera stuck behind our character throughout the level. This time exploration takes a much stronger spotlight in the general game. There are small cutscenes that connect the levels and make the story progress instead of seemingly going through random portals.
This also allows the story to have more moments of humor and character development, however basic it may be. Instead of being randomly teleported into different dimensions where the levels take place, you get to see how they actually get there. There are no warp-zones either, so each level is more connected through the story.