This is a generalization, but the stability of the bare tractors are probably not all that different. The larger rig gains an advantage when you start adding attachments or payload. For example, you may be able to pick up the same 500 lb. stump in your loader with both a big and a small tractor, but the bigger one will be more stable in actually carrying it someplace.
All other things being equal (tires, 2WD vs. 4WD, etc.) a 35-40 hp tractor weighs considerably more and will have an advantage in traction. It will pull or push objects a smaller tractor can't budge. But, being heavier, it's also not as good for mowing your front lawn!
Of course, knowing the limits of the equipment is equally important whether it's a large tractor or a smaller one.
Just as a suggestion, maybe you can itemize the specific tasks you need to do, or the ones that your current tractor doesn't measure up to, and use that list as a guide for determining what size range you need to look at.