For this test I compared my Nikon D750 w/ 24mp FX sensor to my D3300 w/ 24mp DX sensor. I used the same lens, a Nikon 50mm f1.8 AF-D and built in flash. The top row is at ISO 100 to show the best resolution, the lower row is at ISO 6400 to show noise. The distance to the target was 51" for both cameras but because of the 1.5x magnification factor of the DX sensor the size of the target at 100% magnification in Photoshop yielded a 2x3" target for the FX vs 3x4" target for the DX. I resized the FX image to the same size of the DX. The pixel size is identical for both sensors, this lens is capable of resolving over 100 l/mm.
Draw your own conclusions.