It would be interesting to know which lenses you used on the E-M10, but while I made good photos with the 6s, in general they wouldn't compare to what I consistently get with mFT. The size difference between mFT and APS-C is neglible compared to the difference to the smartphone cameras.
Where the iPhone shines is getting nicely automatically post-processed pictures. Olympus has an iAuto mode, which also aims for that. There are also a lot of in-camera settings where you can tweak the produced jpegs, if you don't want to post-process. The best quality you would get though by post-processing raw images on your computer.
Yeah, I'm curious too. I've got a E-M5.2 and the photos I get on it are consistently better than what I get on my Xr. I mostly shoot in Aperture priority mode, but I switch to full manual in tricky situations. I do very basic editing with Darktable.
Before I bought my E-M5.2 I had an E-PL2, looking at some of the pictures I took with the kit lens they are generally still better than the pictures I've taken on my phone.
I used mostly a Lumix 20mm 1.7, plus the kit 14-42mm and 40-150mm. As far as I know the sensor is the same in the EM5.
Of course the camera gives a lot more creative freedom, but it felt pointless to carry a body + lenses for little improvement in quality, light as they were. I switched to a Fuji XT-2 and am much, much happier.
Where the iPhone shines is getting nicely automatically post-processed pictures. Olympus has an iAuto mode, which also aims for that. There are also a lot of in-camera settings where you can tweak the produced jpegs, if you don't want to post-process. The best quality you would get though by post-processing raw images on your computer.