I like Puzzle League more because it involves more skill and it's faster paced, but Desert Island Escape is okay if you like strategy games which involve a little luck.
With Puzzle League, you can play in chunks and put the game down after a few minutes if you'd like. It isn't all about luck and doesn't cost 6 Play Coins to play every time if you don't have Amiibos! Both games are nice, I just prefer Puzzle League.
I haven't actually tried Island Escape yet (gonna be giving my nephew my ds to run around with tomorrow I think ;p ), but I do like puzzle league. Even if I can't get past the 2nd level! I will......
The puzzle game is addicting, but it makes me want to die half the time, so I'll go with Desert Island Escape as my favorite. There's more to do in it, anyway.
I almost selected "I hate them both" because both games are honestly so hard for me xD But I actually like them. I completed the puzzle league pretty fast but i like to come back to it from time to time. But I like Desert Island Escape more because it's more complicated. Also I love seeing my villagers for once do something else than just wander around town and occasionally water flowers.