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When comparing these crops, however, you have to keep in mind that neither of these is actually shot at ISO 6400. Manufacturers typically label a lower ISO as ISO 6400 (and this is actually true for all labelled ISOs). Although I do very much like the OM-D that I got my partner. Olympus has been particularly egregious in its labelling of ISO. According to DXO, the measured ISO of the shot below which is labelled as 6400 is only 3024, Sony mislabels as well but not as much. The measured ISO (again according to DXO) of the labelled 6400 for the NEX-7 is 5401. So really this is a pretty unfair comparison. The NEX-7 is shot at ISO 5401 and the OM-D is shot at ISO 3024. So, it isn't really surprising that the OM-D looks quite a bit better. The NEX cameras (and there isn't really anything to talk about in difference between them) when shot at the same actual ISO (and not labelled ISO) are a bit better than the OM-D, but only about a 1/3 of a stop. Given its smaller sensor the OM-D does remarkably well. In use I find the labelled ISO of 3200 (actual ISO of 1489) to work well for even 11 X 14 prints and most web application. I find the labelled ISO of 6400 (actual ISO of 3024) to work fine for 4 X 6 and with careful processing 8 X 10 prints and web presentation. When my partner got the camera I switch auto ISO to the labelled 3200 instead of 6400, because I didn't want to loose important shots to too high an ISO. Still it does quite well and at least as well as my old Canon 50D (and DXO measurements agree with this assessment). Nevertheless, all of these cameras fall far short of full frame cameras in this regard. Full frame has a stop to 2/3 of a stop advantage over any of the smaller sensors in high ISO when you look at actual measured ISO.
In fact, here's my comparison shots that I did in dim lighting between the two cameras when I had the NEX-7. The color is more accurate here in the OM-D image, as the thread was really that color maroon. They are similar per pixel, though the OM-D seems to resolve a little more of the thread. The funky pattern in the lower left is the wood grain of the table, BTW, not some odd noise patterning.
NEX-7 @ ISO 6400:
OM-D @ ISO 6400: