If these are the choices and only these, I'd do the following:
Leica on .338, use that for deer. More rifle than necessary? Yes, for sure. But that scope and rifle combo makes sense and you indicated having an inclination toward using it, and more importantly the low end of that scope is much more suitable for short range deer work.
After that, put the Leupold on whichever of the other two you like better and/or do more target work with, as it should hold zero and track much better than the vortex. I would put it on the .308 for such things.
The vortex then goes on the .243 for varmints and such with the higher magnification. Less recoil should help it last longer as already suggested.