The later good ones (mid 80's) have BIG CAM casting letters on the camshaft side of the block, which is the same side as the injection pump/air compressor. I also believe the cam follower boxes where larger on a Big Cam--maybe crenwelge can confirm this. The small cams were a little before my time--either wrenching or driving.
My favorite Cummins is a Big Cam III. They were a good dependable engine. I didn't like the cooling system on a Big Cam IV. Heat is the arch-enemy of these old Cummins engines--they don't tolerate temperatures much over 180 for very long