Will the existing supply wire for my 60A subpanel be adequate for a 100A subpanel?
To identify the wire gauge, the best way might be to take the cover off of the breaker box (advise to do this with power off for safety, but power can be left on - proceed at your own risk) and see if there are any indications on the wire sheathing.  If there isn't, use a guide like to identify the gauge of wire.




As for copper vs. aluminum wire, aluminum might be cheaper in larger sizes. However, aluminum requires some special anti-oxident joint compound when you make connections with aluminum wire (see Ideal no-alox for an example of this stuff).  If you don't use the compound, its possible that the connections will fail over time.



EDIT: Using the info you provided in the comments, and the wire voltage drop calculator at http://www.southwire.com/support/voltage-drop-calculator.htm, assuming: 
 - Single Phase 240V 
 - Direct Burial 
 - no more than 3% voltage drop 
 - 2 AWG aluminum wire 
Your wire gauge will allow you to maximum run somewhere in the 75-80 amp range.  I wouldn't go all the way to 100 amps, but 60 amp service should work.  You'll need 1 AWG wire to run 100 amps safely that distance.