I've wanted to try this for a while and finally got around to it today. It's very simple. I put the very same
50mm lens on two cameras (FF & APS-C) and took two photos at the same distance (~ 80 cm), and the same f-number (f/1.4). The results are predictable but perhaps enlightening to someone fresh to photography.
I used my old Lenscal focus calibrator with scale markings adjusted for a 45° angle, ie, the distance between each major hashmark measures 1.4 cm. So the "2" numerals on the scale are 2 cm in front or behind the target.
Full-frame camera (A7RV, 61 mp):

I'll say the DOF is about ± 2 cm. People with better eyes might say ± 1 cm or even less. Hover your mouse pointer over this photo for EXIF info.
APS-C camera (A6500, 24 mp):

Looking at the scale the DOF measures the same to me. Hover your mouse pointer over the photo for EXIF info.
So when someone says "APS-C cameras have more depth-of-field." what do they really mean? If we measure it with a scale, the DOF seems to be the same.