Just off the top of my head; ZT has an inch more in length in Sandvik steel. The ESEE is 1095 carbon steel. The ESEE has a bit more belly offering more utility (read deer hunting like in your original post). The ZT has G-10 scales versus the ESEE having Micarta scales. Both have a black coating on the blade but I think the the ZT has the DLC coating. I think it's a bit nicer than the duracoat type coating (I think?) on the ESEE but just my opinion. Both come with nice sheaths.
I bought the ESEE 4 about a week ago to take with my as my utility blade for deployment that I leave for this coming weekend. It's thick, tough, sharp as hell, MOLLE compatible and not too heavy. I've played around with it around the yard just to get used to it. It's just an outstanding knife. It just does everything I need it to do; chops well for a 4" blade, batons very well, fits well in my hand and really holds an edge. I like the 1095 steel too for re-sharpening. Gets razor sharp rather easily. It's well balanced and I like the finger choil. I think I covered everything.
All this said, I haven't personally handled the ZT. I love their line but I had to go with ESEE. These are just my opinions and observations. Get what you like and enjoy it.