All stone will need to be compacted prior to pouring a slab or you'll have that slab cracking in no time. As far as a slab being an easier way to clean out manure, sure, if you've got a bobcat. If you're still doing it by hand, then no, it won't be any easier at all. Remember you'll also have to provide a continual supply of shavings or straw as a bedding surface on top of the concrete or your animals will get scrapes and sores. That's an additional ongoing expense that you will be adding as well as the one time cost of the slab.

I would think a 4" base of stone over polyethylene would be
fine. You would also need some expansion joints every few feet.

In a slab an expansion/isolation joint separates the slab where it touches another structure.

A contraction/control joint weakens the top fourth of a slab so that a crack would occur there instead of randomly and are placed much farther apart than every few feet depending on the slab reinforcing and how the owner feels about cracks.

The crushed stone should be placed over undisturbed soil.