The larger the wire the more current it can handle, with heat loss, heat does no useful work and consumes energy..so It is always a useful thing to go as large as practical when replacing the wire..
On the alternator winding..Why go there, you can probably upgrade to a higher output alternator as cheaply..
There are basically two ways to wire a 3 phase alternator, star ( or Wye) and Delta. With Delta you get lower voltage but more amps. In star you get higher voltage but less amps. You can calculate these by using the square root of 3 ( or 1.732 ). Each coil set is a "phase" of the alternator so when you measure voltage,ohms or current to test one phase of the alternator you would measure the "phase". Once you know what the output will be from one phase you can calculate the "line" output of either delta or star.
For more on Alternators:Alternator Basics
Read this and decide..
Remember, how ever more you bump up the output, your internal components must also be upgraded if they are to last..