Ok for starters the Mini Y is shorter. I have shot both and they both work just fine. You just have to decide if your looking for the recoil reduction or a 'cool, but legal'(ie, fake FS) look if using on a postban.
A good comp is LOUD. Its not really bad when you are shooting but your buddy standing behind you or off to the side will probably complain.
Lots of people get rid of their comps for this reason coupled with the fact that recoil from a 223 really isnt bad at all. Simply the annoyance from the blast, etc. outweighs the gain in recoil reduction for them.
I like comps. I shoot alot of 3-gun type stuff that requires fast, accurate and multiple hits. Comps make this easier and faster. If I were going to shoot varmits from a rest or prone, I would not use one -- the blast and extra noise would outweigh the gain that I would get. However, if youre looking for fast follow-ups the comp route is the way to go.
The mini -y works great and does the job well both in semi and FA. The best comp I have found for the reduction of muzzle rise and recoil is the ZM weapons y -comp. Down side is they are about $100 (at least last one I bought from them was) and they are longer - about 2.5-3 inches (which bothers some people as it doesnt look cool,tactical, bad, mean, etc.). With this comp my rifle doesnt move vertically at all. Its loud and often annoying to the old guys that shoot 6 rounds a hour while drinking their coffee and bitching about how BAD the world is now, but IT WORKS for its intended purpose - decreasing muzzle flip and recoil.
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Hope this helps.