I believe Passport beat me to it but here is a simple, albeit imperfect, test
-Take two cameras with identical processors, flange distance, pixel count, and lens, but with camera A having full-frame, and camera B, an APS-C sized sensor.
-Place a high-res blowup of the first page of War and Peace on the wall, and take a photo with each camera, at the same shutter speed and aperture, from the same distance away (at an optimal exposure, of course), so that the page fills the frame of camera A.
-Make a 200x enlargement [print] of each photo [file].(camera A = 360mmX240mm, and camera B = 222mmX148mm)
Take a pair of scissors, and cut down the camera A print so that it matches the framing (size) of the camera B print.
Compare prints for sharpness.
Finish reading War and Peace.