It seems to me, caulking on the inside would be less likely to cause moisture in the walls than caulking on the outside.

When you install insulation with a vapor barrier, you're supposed to put the vapor barrier toward the inside of the house.

Since it's an apartment you're talking about, Mortite makes sense. It's removable. You put it on in the fall and take it off in the spring, when you want to open your windows.