What's the difference between 128x128,256x256,and 512x512 head textures?

512 is higher quality, afaik.

Its not only higher quality. You also can add more details to the 512 head textures because you have more place for details.

They are also sexier, because there is less jagged edges.

Basically in 3D Graphics theory, the higher the resolution the higher detail it will show.
I do reccomend you the 256x256. It has decent quality and a good price.
128x128 is bad. 512x512 is awesome but only can be affored by people with budget of 200,000 TC or more

Higher Res, Higher quality in-game.

Like there are no blurred edges, lines and the like in 512X texes compared to 128X.