The "BIOS" stored on the BCM50 main board is updated when you upgrade a system from BCM50 release 3 to release 5/6. There is no difference between 5 and 6.
There should be no problems with booting newer image on older system. You won't be able to boot older image (e.g., release 3) on a newer system (release 5/6).
Your problem in this case is not the image itself - it is the device (hard drive) that you used. Most likely the drive you have is recognized by the R6 system, but not recognized by the R3 system (its "BIOS"). BTW - I just connected a drive with the R6 image to my BCM50 R1 system - it booted without problems.
I'd like to add a word of caution if you consider bypassing the R3->R6 upgrade by changing the drive to R6 and getting updated keycodes. The upgrade process (besides the logical update of the software on the hard drive)
a) updates the "BIOS" code on your BCM50
b) makes configuration changes that are required for certain R6 features (e.g., booting to the safe OS)
You'd skip these two steps. The result would be a BCM50 system that runs R6 image with R3 BIOS and R3 startup configuration. This combination is fine for a normal use, but the system may not behave as designed if you want to do some "low level management tasks".