My first thought would be that the recoil would increase.

The amount of energy expended is identical (or close enough to call it so)
So as the mass it is pushing against increases so will the "equal and opposite reaction" (a.k.a. the recoil).

Look at it this way: if all of the powder's energy were expended against an immovable object - say a rod inserted in the barrel with the other end attached to a brick wall) then all of it would be converted to kinetic energy pushing the gun backwards. Of course in the real world that would result in a destroyed gun, but it illustrates the logic of why the recoil would increase.

So expending the same energy against a heavier projectile will result in a proportionally higher reaction force = more recoil.