A question about amperage

[decojoe67]

I have one simple question I hope someone can answer for a collector that is not electronically adept. If I used a 6V/4amp lead-acid battery for a '20's radio's A supply (with #12 gauge wire) and could not get audio out of the horn speaker, then upgraded to 6V/12amp battery and did get audio with the rheostats turned-up full, would upgrading to a 6V/20amp battery be to my advantage in any way or just a waste of money?