If it has wasted hay mixed in, or bed with straw, the manure fork would be best in my opinion for the initial mucking out. Better penetration into the packed manure. It won't clean it 100%, unless you get under a packed mat, and it all comes up in one piece. The grapple will allow to clamp on to it, and break it free. You better have a decent spreader though, as those big chunks getting crammed through the beaters can cause damage to it.
If you have QA buckets, you can switch to the regular bucket for final cleanup. That's what I do here for my horse paddock. They seem to waste a certain amount of hay no matter how good it is. Mixed in with the manure, then tramped down makes it pretty hard packed on the bottom. The straight edge bucket is tough to get hooked underneath it, and jump over top. Granted, mine is one of the baby Bobcats with as 36" bucket, but sure beats a pitchfork..!!