If you really research flash threads on POTN, back 6-8 years ago it was very common for photographers to have to dial in FEC +1 by default, in order to get a flash exposure with the same density as might be obtained via ambient-only shot (on tripod). That was true on my 20D. Then, with my 40D and the same flash unit, on ETTL it was no longer necessary for me to dial in FEC +1 by default!
The OP has a 5DII, however. The difference in flash density very well may be attributed to the camera's flash programming, and how it decides about what zones to bias, etc. in commanding the ETTL flash to output a certain amount of light.
In order to prove that a larger format camera does NOT 'need more light', the flash should be put on Manual flash (not ETTL), and the cameras should be set with a manual shutter speed and aperture, and a flash shot taken with each camera...the results should be nearly identical for density.
Keep in mind that in a true comparison, one needs to keep in mind the need to choose FL to suit the format size! So if you use 30mm lens on APS-C (2 * frame height), you need to use 48mm or so on FF (2 * frame height), to frame the same area from the same camera position.
Also keep in mind that the zoom head of the flash may not be truly 'equivalent' in coverage area, when switching between two formats. So a way to eliminate that as a possible variable is to simply set the zoom head at a fixed wide position (like 20mm) for both formats, so that flash coverage angle is identical for both shots.