In a simplified view disregarding drag, and we're only looking at the energy conversion, there's no difference. Mass is the same power in both energies, (mgh and .5mv^2) so it just cancels out and disappears if you're converting between them.
If you introduce drag, then it could go either way based on the particulars. If induced drag considerations predominate, (high wing loading, low aspect ratio, swept wings, high-G pull) then the heavier plane will suffer more losses. If parasite drag considerations predominate (low wing loading, straight wings, low G pull) then the lighter plane will be decelerated quicker (a=F/m, or why the golf ball will fly farther than the ping pong ball)