Some differences:
- SDI has a student manual. PADI does not. (PADI has more "lecture".)
- SDI requires students be 21. PADI accepts 18-year-olds.
- SDI requires two dives. PADI requires three.
- PADI requires redundant depth/time devices, redundant signaling devices, a cutting tool, and slate. SDI discusses these academically, but does not list them as required equipment. They were required for my certification dives, including a pony.
- PADI requires a 2-minute, 60 foot underwater scuba swim without mask. SDI does not require mask replacement at all. < But at least one SDI instructor (mine) does. > I had to do a mask swap on every dive.
- PADI requires SAC be determined in the water. SDI allows it to be determined out of the water.
- PADI requires navigating to within certain limits. SDI simply requires proficiency.
The biggest difference may just be the name.
Interesting -- your conclusions differ from how my course was taught.