From the test build I've made, the thinner the wire the better was the bass spectrum. My understanding is that the thinner the wire the more the whole cable act as a solid cables because the strands are more in electrical contact with each other as opposed to larger strands. Being more stiff, the larger strands will push off each other resulting in a sound more akin to a litz cable configuration.
Resistance of wire is not linear, at low frequency it is function of the diameter of the wire and as frequency rises inductance takes over and the resistance rises. A larger diameter conductor will reduce the low frequency resistance, shifting the tonal response toward the lows end.