Quick summary: For a loud show, send the mics through a battery box or preamp into line-in. A battery box is all you need for loud amplified music.
Here's why:
A Mic-in jack does two things. It provides power (Plug-in power on the PCM-M10, a few volts) to the mic and it sends the signal through a built-in preamp.
The Line-in Jack, meanwhile, is for a signal from something amplified or powered, so it provides neither power or preamp.
Going through Mic-in, overload can happen at two different spots in the recording chain:
1) It can happen at the mics themselves--mics can only handle a certain sound pressure level (volume), particularly in the bass.
2) It can happen in the preamp, and again megabass is the quickest to overload it. If you had the mics at Hi Sensitivity, the preamp is boosted higher and overloads faster.
To help prevent (1) you provide more power to the mics, either through a battery box (which is generally all you need at loud shows) or a preamp (which, turned to zero gain, is essentially a battery box); more power helps them handle higher volumes.
(2) To skip the built-in preamp in the unit, you go through line-in with a better preamp or a powered signal (via battery box) from the mics. For loud shows, a battery box into Line-in works well because it's loud enough--you don't need amplification from the preamp.