I have a Yamaha WR250R dual sport, a Yamaha Grizzly 450 4x4 quad and a Polaris RZR 570 50" trail UTV.
I haven't ever hunted using the bike, but have scouted with it and there is no doubt you can cover more ground faster on the bike in good weather. It can be a challenge for me on some of the more technical trails that are very rocky and steep. Some of the trails I am white knuckling on the bike are relatively easy on the quad or rzr. Going down is always harder than going up. There are a few motorcycle only trails, but it never seems like they are in a spot that I really want to go. They are generally pretty short out and back options as well, not many big loops or anything like that. If you got any snow on the ground you would be in trouble on the bike on some trails. I ride mine with a light pack, but I think you would need to be a pretty good rider to ride with a heavy pack. Even riding with a light pack took some getting used to.
I really enjoy using the RZR especially if hunting with a buddy. I have a rack setup on the back of mine that will let me haul enough gear for 2 people for a week on it with no problems. It gets good gas mileage and has an 8 gallon tank so I can easily go 150+ miles on a tank of gas, my ATV has a 3 gallon tank and is limited to 50 or 60 miles before I need to fill up. I had a full cab Ranger before the RZR, and while the cab was nice in the cold, it got hot in the summer and added a lot of weight. Also you can't take a Ranger on any of the 50" trails and it seems like there are a lot more 50" trails in several states lately. There are some 50" ATV trails you can get way back in and setup a base camp and get into some pretty good country. Having the RZR back at camp gives you a lot of peace of mind knowing you could haul something out if you got it down way back there although I have never shot an animal that I've actually hauled out with one!
The ATV mainly gets used for recreational riding now. We bring it along usually and let other people ride it. It can get used if you need to do a drop off at one trail head and hike to another type excursion.
Actually I use all of them more for recreational riding than hunting.