I agree pretty much 100% with Baron Hazard. But I will add that I love fact that FATE is so customizable. As much as a like storytelling and improv, both of which FATE is much better at than any other system I have played, I like designing characters even more.
In D&D 3.5, when you design a character, you are basically checking off a list of boxes with pre-built feats/spells/skills. Most groups would not let you make up your own feats or spells, largely because the balancing of the components on a character were so opaque (the difference between spell levels, especially in the middle, seems completely arbitrary, and feats vary wildly in power). Since there is no real mechanical impact of back-story or personality on the game, hardly anyone takes the time to make them. In the end, character creation is like building a puzzle, you try to fit the pre-existing pieces together so they work (and often there really is only 1 optimal way to do it). This is boring. Further, the combat takes forever and is very mechanical, and this makes it hard to tell the story.
In contrast, DFRPG forces you to create your own spells, encourages you to make your own stunts, and has no problem with creating new powers. Further, aspects for you to at least consider your character's story and personality, and give you a real game play incentive to go much deeper. The only real qualm I have is that some of the skills are much less useful than others, I normally fix this by just combining some of the redundant skills together and reducing the number of skill points (I have never had any of the problems with balance that others seems to complain about). Well, that and how Feeding Dependency or Demonic Co-pilot work.
The game play is also just more fun for me. If you really like mechanical simulations, where every action has a number and associated rule, then FATE isn't for you. But if you just want to tell a story with an element of randomness and suspense thrown in, FATE is your game.