Attached you find two screenshots depicting the results of running both Kaiten/K9 and Aqua Mail for one hour in background with all connectivity switched off. Neither of the two apps were used in the time, the phone's display was switched off.
Given above scenario, Aqua Mail consumed .20s CPU cycles. In contrast, Kaiten consumed .08s CPU cycles. For both apps you can look at the charts how the cycle usage is distributed for each app.
I am sure there are better ways for an even more accurate analysis, like using Android's built-in debugging tools, but this gives you a quick picture.
Another important tool is BetterBatteryStats which I mentioned in the last post. It shows when and how often apps wake up the device from its sleep cycle. Generally Aqua Mail is behaving very fine here in comparison to other mail apps like K9, but I have noticed a few spikes in partial wakeups caused by Aqua Mail, and am still trying to find a way to reproduce them.
Cheers