What and how big is the difference between 600mAh adn 800 mAh battery?

Anyway, the 800mAh batteries will last longer than the 600mAh ones because they have more storage capacity.

See: http://www.greenbatteries.com/nibafa.html#mAh%20defined

Anyway, you can get even better batteries (up to 1000mAh) here: http://www.thomas-distributing.com/aaa-nimh-batteries.php

You will notice a big difference in play time between 600 and 1000. The bigger the better.