Length of string and its break-angle over the bridge affect string pliability and, in some cases, could affect resonance and/or sustain. The original idea of the adjustable stop-tail was to be able to adjust the pliability of the string. In old Gibson literature that came with the guitar, you can see instructions for how to adjust the stop-tail to give you a "slinkier" feel when bending.
Top-wrapping is usually done so people can screw the tailpiece down to the body all the way (which, in theory, gives you more of... something...). But by screwing the tailpiece down, the strings cut into the back of the bridge. So, top-wrapping solves the problem by decreasing the strings' break angle so they no longer come into contact with the back of the bridge. The "slinkier" feel comes from both the decreased break-angle as well as the longer length of string behind the bridge.
One thing I don't understand, though, is WHY it's bad for the strings to come in contact with the back of the bridge in the first place. If it's to keep the strings from forming a groove in the bridge... then it's a silly solution because top-wrapping causes the string to form grooves in the tailpiece all the same...
Same thing goes for the nut/headstock. The break-angle off the back of the nut to the tuning pegs will affect string pliability, resonance, sustain, "tone," and etc. And that angle is dictated by headstock angle.
THE MORE YOU KNOW, BITCHES!