Does a Sigma DC Lens equal to a DX Nikon lens, and a Sigma DG lens equal to a FX Lens?
Yes, you’re correct. See http://www.sigmaphoto.com/lenses/lenses_chart.asp and scroll down to the bottom where it talks about DC lenses.
I suggest you look at www.slrgear.com they have extensive tests on many lenses, nikon as well as sigma. Check out the chromatic abbrasion, vignetting and sharpness charts.
It’s the place I go to when considering new lens options.