I love Fate, but Fate is not a game one can easily pick up and play as it is out of the book. Fate is a skeleton of a game that needs you and your players to fill out the details before you can play it properly. If you want to run Shadowrun in Fate, you're going to need to either find somebody who has written that hack for you, or hack it up yourself. Fortunately, if you want simple, Fate can do all of that with simple unified mechanics and you can get a lot of the Shadowrun specifics covered by Aspects, Stunts, and additional Skills. To Fate's credit, that skeleton allows you to set the dials of complexity at a range of places depending on your taste but, again, somebody needs to do it. If you put in the effort, though, you might find Fate is the best system out there for creating a gaming experience that resembles a novel or movie. It is darn fine narrative simulationism.
For other options:
Savage Worlds has been mentioned and that's about to get a new edition released and that edition is lookin' good. There's also supplements to cover sci-fi and fantasy so there's less legwork on you to make Shadowrun happen in Savage Worlds. Interface Zero also just kickstarted a third edition and that is kind of the go to Cyberpunk for Savage Worlds. I've heard of people using Interface Zero and the Fantasy book together to run Savage Worlds Shadowrun.
Finally, there's a great hack for Genesys for running Shadowrun. If you don't mind the custom dice, Genesys is an excellent system that I think would be nigh-perfect for Shadowrun. It combines a satisfying level of crunch with numerous narrative based widgets that players and GMs can use to keep the game moving and flexible.
