A question about amperage

[madlabs]

The only thing I can think of is that the battery was low on charge and the voltage sagged. Or perhaps that you had a poor connection and when you connected the other battery you remedied it. Have you repeated the experiment, meaning connect the 6 aH battery and found that once again you do not get full volume? If you do, measure the voltage before and after turning the radio on and see what you get.