I would certainly think that using a guide would increase your liklihood of taking game.That's their profession,what you are paying for is for them to put you on game.If you hunt with a reputable outfitter your liklihood for success should be the greatest,they know the area,they know how the game use it,they have been scouting and they should have a pretty good sense of what an area holds.
You would think that private land would be more productive than public but that isn't always the case.Depends on where it is and how hard the hunter is willing to work to get to it.Where land is easily accessible private would logically be better.