Well, just so happens that I load and use both those sizes for most of my social work.
Here's my question back to the OP....why not use both?
I've used OO Buck on critters and I shoot #4 Buck for song dogs and any other varmint I'm after. Both have merits and will work fine.
My current loading in the Benelli M2 is 3 rounds of #4 buck, followed by 2 rounds of nickle plated 00 buck. I leave the chamber open with a round of 3" lead BB ready to stuff in it. This way I'm ready to kill a raiding Raccoon, or Coyote in the back yard (I live way in the country) or am set to deal with a two legged varmint as well.....
Good luck