I haven't played FATE so I can't comment on the comparison, nor do I know what a FATE-ish approach is.
I will say that Anarchy is extremely flexible, with large degrees of latitude provided to the table to define the roles of the GM and the players. If you want everyone at the table to be a mini-GM, you definitely can. If you want a more traditional approach of the GM as a centralized authority and the players reacting and responding to the game world, that works wonderfully well too. Or you could find a point anywhere in between on the spectrum of player agency.
I like Anarchy a lot and would recommend it. There are things that I think could be improved, and I have house rules for most of them, but overall I think it's a positive addition to the Shadowrun gaming community.