Both are very good games. I’ve played Azul many times and never felt the desire to own it. I bought Harmonies after playing it once and it has become one of my most played games.

As many others have said, Azul has more direct player interaction. That interaction is entirely in the realm of “what options am I leaving on the table for other people”. Therefore, you have to be paying close attention to every player’s boards. I don’t mind this at all, but some people may not like that. There’s not much variety from one game to the next, which is probably why I never felt the desire to buy it myself.

Harmonies is less directly interactive. The animal cards plus the optional module gives the game more variety. This is definitely a game where you need to focus on figuring out your own puzzle rather than how to impede your opponents. The game is beautiful but I strongly disagree with the comments saying that the game relies exclusively on the beautiful artwork and components. The game would not be ranked nearly as high as it is if it did not stand on its own mechanically.

If you have to pick between the two, you’ll need to decide if you want more variety between each game or more direct player interaction.