From the player side of the table, there are a number of things that Fate does incredibly well.
Firstly, the almighty Aspect really makes you feel like you have a lot of personal control and creativity invested in making a character. There's just no comparison between a system where you write down a few numbers and perhaps choose a single special feature for your character and one where you get to describe a character in terms like I Have Seen the Dragon and Initiate of the Seventh Circle.
Writing Aspects for your character is also writing things that are now true about the campaign world. Maybe the GM never pictured there being a circle of wizards called the Seventh Circle, but now they're an important part of the world. Declaring that your Trouble Aspect is Nazis! I Hate These Guys! is a formal demand for the GM to include Nazis in the game, and for them to appear regularly. That kind of formal authorial power being handed to the players is really heady stuff, and one more games should embrace.
Secondly, character creation is also explicitly creating a group template between the player characters. The PCs must explicitly have connections between two of the other PCs, explaining how they know each other and perhaps what their relationship is to this point. That's a great starting point to creating HTHD play, and making a group that works together.
Thirdly, the way the game plays out encourages players to be creative and tackle problems in the way that interests them best. They can create Aspects on the fly that will help solve a problem in a way that the GM might never have expected, and that makes players feel good about their contributions. Caught in a dungeon with no visible way out? Create an Aspect called "Hey Guys! A Secret Passage!" or "I Wonder What Happens When I Press This Button...?"
Fourth, when the players are engaged in a conflict of some kind, they are encouraged to cooperate in order to take out the larger threat. The way things often play out in Fate is that the entire group will work at putting Aspects in play so that the person who's the prime mover in the conflict -- in a fight, it might be the best warrior -- can make a single, big hit (rather like a Finishing Move at the end of a martial arts video game) that takes the opposition out. Again, this lets people who aren't even that good at the conflict in question make a meaningful contribution to the action. When we played in Colin's post-apocalyptic monster hunter game The Core, my character Magnus was the only real fighter in the group. But whenever we got into a fight, everybody was able to help out by doing what they did best. That's nifty stuff.
So you say you're not one of the Fate faithful, after three days of me rattling on about one of my favourite games? Well, maybe direct exposure will change your mind. After a successful Kickstarter, Evil Hat has made the new line of Fate books -- including Fate Core and Fate Accelerated -- available on a Pay What You Want basis through DriveThruRPG. If that's not enough to get you to try out these games, I don't know what is. Pick up Fate Accelerated and give it a spin. You will be happy you did.