I find that Sagrada is a better game when you've got players of mixed ages and skill levels playing -- it tends to be much more of a level field because the strategy doesn't matter quite so much between rounds unlike Azul. The scoring system in Sagrada is also a little more straightforward in that its pretty obvious how to maximize your points. The game is also generally less adversarial than Azul, which is good if you're trying to do a couple rounds after a family dinner or something. It ends up being a little more of a game you can share a drink or a dessert over -- whereas Azul quickly turns competitive.

Basically, Sagrada's the game I bring to family gatherings, Azul's the game I bring to board game nights for a warmup/cooloff game.

With Azul, it's basically the same puzzle every time, and you're dealing with the particular order in which things are available. Sagrada's goals and special moves switch out every game, which makes each game its own puzzle. This adds a lot of replay value for me, though there's also a lot of random variance in the puzzle difficulty: sometimes it's a very easy puzzle and everyone gets near-perfect points, and sometimes it's deliciously difficult.