I think the answer might not be as clear cut as you're hoping. Life's never that easy!
I made this decision earlier this year. Sounds like a similar application to me though I was never that confident that either would really satisfy for fast moving kids.
The things that prompted me to go for the EM5ii were:
- Hi res mode. This was a big draw for me. Many people don't seem that bothered about this but I personally love it and have found it far more usable than I'd perhaps envisaged. It's true that it doesn't work in lots of applications but for landscapes, I've found it works more often than not. A small amount of movement in shot at relatively quick shutter speeds can throw up some silly effects but when you're using longer shutter speeds and movement is more fluid (flowing water, moving clouds, grass blowing in the wind etc, it all blends okay in the same was a single long exposure looks.
- It's smaller. I like the fact that it's pretty discreet but doesn't lack in the control department. It's lovely to carry with no grip and just a 17mm 1.8 attached.
- It looks nice - I know this one is unimportant but I like the more retro appearance of the EM5ii.
- Long exposure noise. I have no direct comparison experience here but I'd read a lot of complaints about long exposure noise on the EM1. The EM5ii is no full frame performer here but I find it perfectly okay.
- The live composite and live bulb modes. These are great but not sure if firmware updates have now brought these features to the EM1?
Things than almost made me opt for an EM1
- Better AF performance for moving subjects. I honestly don't know how differently they perform but I get the impression the EM1 is better but maybe still not what everybody would hope for.
- Better balanced body for bigger lenses. This might be very relevant to the 12-40, although of course the EM5ii can take a grip.
- Better direct button layout. The DSLR style body puts everything more conveniently at your finger tips.
- Focus stacking in camera. This wasn't actually a consideration at the time as it wasn't announced but is a nice feature. The EM5ii does focus bracketing but you'd need to stack in software.
- Being able to effectively use 4/3 lenses. I don't have any but the option is nice and there are some stunning lenses to choose from.
I'm sure that's not telling you anything new! It's a tough choice. Not really sure that you can make the wrong decision as they both have some great features but are pretty damn similar underneath it all.