A few observations, in no particular order:
1. My OM-D, at least with the lenses I own, focuses consistently more accurately than any dslr I’ve used (whether Canon, Nikon or – especially - Pentax): provided it confirms focus, the camera accurately focuses on what I asked it to (barring something like subject movement or, if focus is very shallow, movement by me). Regardless of aperture (and I realize M43 have an inherent advantage here), not once have I had an unpleasant surprise of the sort I occasionally get with dslrs. I’ve no idea, obviously, whether that played a part in your comparison – how many times did you repeat the Canon photo? Were you focusing on exactly the same point with each camera? No lens will look sharp if, for whatever reason, the focus is off (unless it accurately focuses on the wrong thing).
2. Back/front focusing isn’t an issue for mirrorless cameras, but it be the problem with the Canon combination you used ( my 6D and 24-105 are quite cooperative with each other, but yours may not have been).
3. For ergonomic reasons it’s easier to adjust exposure right when using an OM-D; and my OM-D tends to be a bit more reliable in that regard too than the dslrs I’ve used (not that I have any complaints about my 6D). It looks to me as though the Canon photo is somewhat overexposed (esp. the top of the lamp), which reduces detail and the appearance of sharpness. Combine that with inaccurate focus and the photo *really* won’t look sharp, no matter what lens you use.
4. Leaving aside whether any focus adjustment was needed or the lens was somehow flawed, you may have ended up with a less good copy of the 24-105. I get the impression from reading this forum that some are sharper than others. (I’ll assume you didn’t accidentally turn off the IS!) I doubt that has anything to do with this particular comparison, though.
5. For some of the reasons already mentioned, and leaving aside whether what you rented is flawed, I and am no longer surprised that one can get better results (at least in some respects) with an OM-D (I was quite skeptical until I rented one). I own a 6D and an OM-D and use both frequently (sometimes together).
6. (This has nothing to do with your specific complaint.) As you’ve noticed, the OM-D is surprisingly good in low light/high ISOs, but beyond a certain point there’s no contest. Likewise if you like shallow depth of focus and smooth bokeh (nevertheless, even though there’s less background blurring with the OMD for any given field of view, you can still get superb bokeh, depending on the lenses you use).
7. (This has nothing to do with your complaint either.) In my experience Micro 4/3 lenses tend to be more prone to chromatic aberrations than the better Canon lenses, and you can see that in your comparison where, whatever else may be going on, there’s a little on the OM-D photo at the top of the lamp.
8. As for other lenses to show off the 6D, try a 70-300L (the range more-or-less matches your inexpensive zoom), a Canon 100L, a Canon 135L or a Sigma 35 1.4 and see what you can see, especially if you care about shallow focus and background blur (though with the latter two you won’t have image stabilization – another area where the OM-D spoils you). And, just for kicks, throw into the mix a couple of the best M43 primes, such as the 75mm 1.8, 60mm macro, 45mm 1.8, 17mm 1.8 (all Olympus), Panasonic/Leica 25mm 1.4.
