I think you may be barking up the wrong tree somewhat...
There are basically two types of distortion which can be seen in photographic images, the first being perspective distortion - the classically bad "big nose" appearance in a portrait. As Alan says, this is due only to the distance from camera to subject and the angle of the subject plane to the sensor plane. Perspective distortion does not depend on the camera format or the focal length of the lens - except that a wider lens might encourage you to get closer and thus amplify the distortion.
The other type is optical distortion, where straight lines near the edges of the frame are rendered as curves - this isn't formet-dependent either; it is governed by the optical design of the lens being used. The FX format doesn't automatically give you less distortion than smaller (or larger) formats. If you have a 24mm lens on your D7000 and a 35mm lens on your D700, one might have less optical distortion than the other, but any difference would be due solely to the design of the lenses. Similarly, a 13mm lens on a Nikon 1 camera might give more or less distortion than either of the others.
In short, there is no generic answer to your question - you'd need some practical testing to determine the distortion characteristics of any particular mirrorless camera/lens combination.