The third book is my favourite as well. I think it's mostly because it's the calmest of the series. The first two are very much about getting to know the world and the enemies, and from four on it's all about Voldemort returning, but PoA is just in between.
It's really about people, friendships, and explaining what happened all those years ago. It also introduces the Marauders (both as actual characters and as part of history with the map), who are still my favourite part of the HP world and the HP fandom.

I've just reread PoA, as well, and I still love it. It's amazing how after all these years and readings I can still enjoy it so much, but I suppose that's part of the magic.