The taller tires do raise the center of gravity but since the taller tires are all much heavier which lowers the center of gravity it's usually a wash on the balance side of things. The taller tires require more horse power due to both the extra weight and reduced gearing and in general, handling and ride are not as good as with smaller lighter tires. A lift kit which some combinations require has never seemed like a good idea to me.
On the other hand though, you gain increased ground clearance and much, much better traction for improved climbing ability and pulling ability through mud. Most larger tires are 6 ply which adds to puncture resistance which can save your day.
I keep on hand 2 sets of tires and wheels. One for mud and crud and just in general craziness the other set is shorter and lighter for fast trailing and pleasure.
