It seems like you asked one specific question, but there are really two things you are interested in:
1) which would hurt more?
2) which would do more damage?
In the first case, there’s no way to say. The full bottle might hurt you more than an empty one, but someone else (with a different shaped head, thicker skin, etc.) might feel more pain from the empty bottle.
There’s also the question of whether or not the force was delivered exactly the same way in all cases (angle, velocity, point of impact, etc.). Unless you’re going to build a "beer-bottle-over-the-head-O-matic"(tm) the characteristics of the impact are going to vary each time, which will affect how much pain is inflicted.
So...there’ really no way to tell which will hurt more, because there are subjective as well as mechanical factors that would have to be dealt with.
As to which would cause more damage? Well, given two exactly the same attacks (velocity, angle, point of impact) then the full bottle is certainly going to cause more damage. As you correctly note, it masses more, and therefore carries greater impact energy.
That covers the damage from the actual impact.
One important remaining factor is whether the beer bottle shatters. If it shatters on impact, and the jagged pieces or remnant still in the attacker’s hand retain enough downward force to gouge the scalp...then there will be additional damage. In practice though, whether the bottle shatters has as much to do again with point of impact, shape of head, etc. as it does with being full or empty.
All things being equal, the full bottle is actually more likely to shatter given two identical impacts -precisely because it masses more and the container therefore has to absorb not only additional energy from an impact at a given velocity on its exterior surface, but also deal with an accelerated mass (the beer) stressing it from the inside as well.
So, with those caveats - I’d go with the full bottle being the less desirable one to be hit with.
