At least your question is a bit easier to answer than the ones which ask "Tribute or Allegiance?" The bows you mention are very diametrically opposed in shooting characteristics. While I've become very accustomed to my Allegiance, and like to think of it as really smooth -- it doesn't hold a candle to the Liberty in the smoothness category.

Likewise, the Liberty can't wear the Allegiance's jock strap in the speed department. Obviously, you're also talking two entirely different cam systems here, and while I was a single-cam shooter for the longest, I now ama huge proponent of the binaries -- if for no other reason than the interchangeable draw module offerings on the Allegiance and most of the others. Being able to switch from the "speed" mods to the "smooth" mods by simply unscrewing a couple Allen screws truly is like having two bows in one.

Ultimately -- and, hopefully, obviously -- you're going to have to shoot these two bows yourself to get a feel for them. You're going to have to decide what's important to you as well. One of the smoothest bows on the planet with OK speed? Or pretty good smoothness out of one of the hardest-hitting bows on the planet?