Next time you tape with a new set of batteries, let them run overnight while recording a radio or something (downstairs where it's not going to be heard) until they go dead at home after the show. You're not losing anything since you throw the batteries away anyway, right?
Note how long each device operates before it goes dead. If the m10 goes dead before the ca-ugly, install a fresh set of batteries in the m10 and then let the ugly run out. Note that you'll probably want to have a 32gb card to do this test assuming you allow the m10 to run without stopping it otherwise your card will fill and everything will stop automatically. Alternatively, before starting the run time test you could select a lower bit depth and sampling rate to get more recording time out of a smaller card.
When I do run time tests like this, I choose a small file size because if you leave the max file size as 2gb and the recorder goes dead overnight or when you're not looking, unless your recorder auto saves files, you'll only know your run time plus or minus an hour.
Probably goes without saying, but the way you know when the preamp goes dead is your signal drops to nothing on the recording. The way you know your recorder goes dead is the total duration of the files that are recorded onto the card before the recorder goes dead.
Since it sounds like the CA-ugly run time is longer than the m10, it will be a little harder to get an accurate run-time on the CA-ugly since you'll need to be there to change the batteries when the M10 goes dead at least once to get a good total run-time duration for the ca-ugly, unless you run the tests separately and plug the m10 into a wall wart so that it never goes dead.