Depending on what you mean by "process".... If you mean gutting, skinning, quartering/deboning the meat for transport, then I like a Havalon Shockey edition with the lockback fixed blade and replaceable scalpel blade. The fixed blade is good for splitting the sternum, separating joints, etc, if you're doing that. If you're not doing any heavy work and you're just taking the meat, the replaceable blade works great. You can separate knee joints with the replaceable blades. You just can't pry hard with them. I use only the Havalon 60XT blades. They're thicker and stronger, so they don't break as easy as the thin blades do, and the edge lasts a good while.
I carry a little mini pair of flat-nosed pliers that I use to change the blades. It's really easy to do with the pliers, and it reduces the risk of slicing your finger if you try to change blades by hand. When I open a new blade, I only peel back the opening just far enough to remove the new blade from the sleeve. Then I put the used blade inside the protective sleeve. If I have an empty plastic water bottle or something, I'll put the used blades in that to keep them safely stored until I can dispose of them.
When I'm doing actual butchering, turning quarters into steaks, I use custom knives and/or my Victorinox boning and butcher knives. Usually all they need is a few strokes on the steel.