It has new music but there's only like two or three songs as far as I can tell. Mainly the regular stage music and boss stage music. I was hoping your amiibo partner would come with their own tune but nope. The cursor movement and block swapping animations seem ever-so-slightly slower than I remember of previous versions of the game, putting it about on par with the GB versions, but once you get into the groove it plays just fine.
It has a Story Mode, which has you playing through something like 25 stages with varying rules, and as you play through Story Mode you unlock Score Attack (endless mode,) Time Attack (2 minutes,) Garbage Attack (endless mode with garbage drops like vs mode,) and Candy Mode (endless, candy is randomly spread around the panels and making a match next to candy destroys it.) Each of those has three difficulty levels and Story Mode has multiple difficulties too.
I don't think there's a Puzzle Mode.
My biggest complaint is that you need to scan an AC amiibo figure to get a decent special power (only AC amiibo figures, no AC amiibo cards, no Villager) which means if you're playing on the go you'll likely have to just use the basic "destroy a horizontal line" special. Each figure has a unique special. I have all except for Summer Isabelle but I've been sticking with Reese because her Special is pretty strong, changing all of the tiles of the most common type to another type when you use it.