I also tend to lean towards wide angle zoom lenses. So the Nikon 16-85mm lens is what I'd probably get with the D7100 and I'd most likely get the 12-50mm for the E-M1.!
I can't help with the body choice, but I suggest you look beyond the 16-85 if you go with the D7100. I shot the 16-85 on my D7000 for quite a while, then upgraded to the 17-55 with constant f/2.8. The 16-85 is nice for it's portability and zoom range, but the image quality is nowhere near the 17-55 or the other comparable 3rd party options (that others here know more about than I do).
You sound like a discriminating shooter. I think you might be disappointed with the 16-85.
I beg to differ. Haven't used or owned a 17-55, using the 16-85 as my main lens though, and I can highlight certain points.
To start with, the price of the 17-55 is ridiculous given it is a DX lens! I consider that robbery! Better off, paying a bit extra and invest then in a proper FX F/2.8 lens. Especially nowadays where everyone would eventually be upgrading to FX soon enough.
Comparing it to the Sigma and Tamron versions, the Sigma in specific, according to DXO Labs, deliver even better optical quality at third the price!
True that having fixed F/2.8 is nice, but the 17-55 sharpness wide open at 2.8 is not consistent at all! It loses sharpness pretty quick wide open over the focal range.
Besides, its performance beyond the 35mm is ridiculous! Nikon should have made it a 17-35 instead. But maybe they thought it would complement the cheap 55-300 better this way.
Overall, its sharpness is not consistent and too focused on the center. Beyond the center it loses too much of sharpness almost all over the focal and aperture range.
Back to the 16-85, it's weakest at the middle of the focal range actually. Talking sharpness again. But consistent on its sweet point of F/5.6 to F/8 all over the focal range. Also retains decent center sharpness all over the range.
In short, while the 16-85 isn't the sharpest lens around, its consistency and very well distribution of sharpness over the bigger apertures and all over the focal range make it more reliable and usable.
Even the cheap kit lens 18-105 delivers more sharpness at some points, but too inconsistent. One has to really shoot at these points (specific combination of apertures and focal lengths) to get that amount of sharpness out of it. The 16-85 is more versatile..
To sum it up on sharpness: Again according to DXO, over 17 mm to 35mm, the 17-55 is mostly sharp at the center while falling out pretty quickly around the center and edges. For this wide focal range, this is not enough! Beyond 35mm the lens is poor. For that price this factor alone makes it a no go. Especially that the 16-85 is consistent over the whole focal range and maintains almost same sharpness within its aperture sweet point range.
16-85 also has VRII! Pretty useful, especially beyond 35mm. For the 17-55, VR isn't a must, but for that price it should still be there.
As to other optical qualities, they are on par. Besides, to me only sharpness matters, as distortion, vignetting, and CA are automatically adjusted in PP, especially when one shoots in RAW.
As to build quality, I have yet to see a DX lens or any lens below the 1000$ range that comes close to the 16-85 in terms of sturdiness and build quality! The lens is simply a pleasure to use. To me this is always a factor of high significance.
Also the extra 1mm at the lower end is significant.
So there you have it. I would always recommend the 16-85, and would definitely recommend against the 17-55 considering that price!