Any time you raise the center of gravity a vehicle will be more apt to tip over.
As the center of gravity is raised, it will move outboard on a side slope. Let's say the center of gravity of a large lifted truck is raised six inches, and you put it on a 45 degree slope. That will move the center of gravity out roughly 5-1/4" towards the downhill side of the slope. Doesn't seem like much until you are at an extreme angle and all that mass starts working against you.
For hard cornering, a raised center of gravity means the mass has more leverage to reduce traction of the inside wheels.
This can be countered a bit by using offset rims or very wide tires to increase the wheel track, but that is a bandaid, not a cure.
The plus side to this is that you get better approach and departure angles, can run larger diameter tires without hitting body work (in theory - some fenderwell openings are just too small), and get longer articulation travel.
Everything is a compromise. Change one thing for the better, and something else will be for the worse. It all depends on how much gain you get for what you lose.