In principle, DOF at a given numerical aperture should always be the same for the same final image magnification (object size on the actual print.) But this would be a tricky comparison to make, since the R-D1 image would be a cropped version of the full-frame 35mm image.
-- Would you compare by shooting a photo with the R-D1, then moving closer with the 35mm camera until the lens covered the same subject area?
-- Or would you shoot both photos from the same distance, then crop the center part of the 35mm image and enlarge the cropped section to the same size as the R-D1 image?
-- Or would you shoot both photos from the same distance and print the full image area, disregarding the fact that objects in the 35mm image will be smaller?
Just to make things more complicated, there really is no such thing as depth of field -- it's an optical illusion caused by the eye's limited ability to resolve fine detail. Since there's no way to view an R-D1 image except on some type of computer output -- monitor, inkjet print, whatever -- your apparent DOF is going to be based on the eye's ability to resolve detail on that particular type of output. So it could be that the apparent DOF of an R-D1 photo would vary according to the way you're viewing it!
This isn't a new problem. Newspapers reproduce photos via a fairly coarse halftone screen (typically 65 lines per inch) that divides the photo into dots that are visible on careful viewing. A side effect of this is that a photo reproduced in a newspaper has somewhat greater apparent DOF than the same photo viewed as a print: the halftone dots break up the image so that slightly out-of-focus areas look just as sharp as in-focus areas, creating the impression that subjective DOF is larger.