I'm digging Marvel Puzzle Quest.
It's a good treatment of both licenses, polished and slick, and has been a good living case study of an evolving, licensed mobile free-to-play app.
The game is free, monetized through purchases in the game, and for the most part, this isn't overly annoying - though it gets there every once in a while (there are distinct "I can't be competitive unless I spend money" moments in the ongoing game events).
Like many free-to-play games, Marvel Puzzle Quest does a good job of rewarding daily play, with the added bonus of character freebies that please franchise fans.
The leveling up mechanic is slick, but the power cap is annoying, and not explained in advance, so you might top out at your aggregate power cap - but not have leveled up the powers you want.
This is less of an issue now that developer Demiurge has added the ability to re-level the powers of maxed cards - a good example of that "constantly evolving" aspect of the game. Plus, it doesn't take a ton of playing to to get the regular, lower-level duplicate cards needed to re-balance maxed characters.
The game is mostly offline, with an asynchronous online mode where you basically play "ghosts"of real players' 3-character squads that fit into a timed theme defined by the game (for example, "Lone-star heroes", which lets you pitch your single star, more common heroes against other players' similar rosters.
The game has turned into my go-to time filler on my phone. Games aren't as quick as I'd like, but they're close.