DXOMark tells the story regarding noise comparisons between the D7200 and the D3X. Normally one would expect a full-frame sensor to deliver a full stop better SNR because it gathers more light than the cropped format, from identical scenes.
However, the march of technology tends to reduce such advantages when comparing a recent cropped-format model, such as the D7200, with the older full-frame D3X.
As Bernard has mentioned, the D7200 has better DR than the D3X, by almost a full stop at base ISO. SNR at 18% is still slightly better on the D3X, by about 1.5dB, but that advantage is not as significant as the DR advantage of the D7200.
On balance and on average, the D7200 image quality should at least equal that of the D3X, noise-wise, and in circumstance where DR in single shots is important, the D7200 will be better. There will be certain situations, such as the requirement for the shallowest DoF, where the D3X will still retain an advantage with a given lens. However, there will also be other situations, such as the requirement for a wide DoF and/or fast shutter speed, where the D7200 will have a clear advantage.
For example, if I'm shooting a scene with the D7200 with 50mm lens at F8, ISO 100, and 160th, the equivalent settings on the D3X would be a 75mm lens at F11, ISO 200 and 160th.
Comparing noise on the DXO charts at these different ISO settings, the DR of the D7200 is about 1.5 EV better, (which is very significant), the SNR of the D7200 is about 1dB better, and tonal range and color sensitivity are also marginally better, which is not significant, but at least we know that the D3X has no noise advantage at all, in such circumstances.
Nevertheless, I have to admit that resolution is another issue. In circumstances where one is able to use a particular lens on the D3X at its sharpest aperture for the required DoF, one would expect the image from the D3X to be noticeably sharper and more detailed than the image from an equivalent focal length of lens of equal quality, attached to the D7200, at least in the central part of the image.
This is a result of the wider pixel spacing of the D3X which makes less demands on any given lens. Ideally, any cropped-format camera requires a higher quality lens in order to deliver resolution equal to that from a full-frame format of equal pixel count, excepting the borders of the image of course, where the cropped format will usually retain an advantage.