Between my amp and my preamp (WS), going battery powered on the amp provided the biggest improvement, but nearly equal. My friend and I both noticed that going to back AC power on the amp, and using an AC powered preamp (my dac), it was a very unpleasant experience and we hooked the battery stuff back up very quickly after that.
When you first go battery you need to settle in and give it a good listen, adjust to the changes, and then you can never go back to gross yucky (untreated) AC after that.
I don't think it matters which component you start with, you will notice it sounds a lot better. But if I were you I would start with my amp.