The alternator can put out a maximum charge of 63 amps. The more amps it can put out, the quicker it will charge your battery.
The battery amps you are quoting are CCA (cold cranking amps). That is the current it can deliver for 30 seconds at -18 degrees C, before it's voltage drops to 1.2 volts per cell (7.2 volts overall)
Obviously the more current it can provide for the starter motor the better. So, in general, the more CCA the better.
Yes, the "520 amp" battery will start the car more "easily".
As far as the car is concerned, all it needs is a 12 volt battery. The more CCA the better!
Hope it wasn't too techy!
h8v.