Fatesinger has alot of ways to increase your ranged damage, and they are what I like to think of as 'static' damage sources. That is, they are reliable and act when you need them to.
On the other hand, Shiradi has alot of random procs, and I believe that one can get up to a 35% chance for something to happen once you get to level 5 in the ED. However, you can't control what procs, and the buffs Shiradi gives to ranged attack and damage are mostly conditional and thus more difficult to gain and use.
All other things being equal, if you had a ranged build that had fully unlocked Shiradi Champion and Fatesinger, which would you use?