How would you all describe the differences between the "courses"?
It really comes down to the instructor, but if you want to blindly stack agency requirements side by side, PADI wins.
First a little disclaimer, I'm not a PADI Self-reliant instructor, but I am an SDI Solo Instructor. I have a copy of the PADI distinctive specialty manual from 2011, which I do not believe is current, however I believe that when you stack the courses side by side, PADI's is more rigorous.
Off the top of my head, PADI requires 3 dives, SDI requires 2. PADI has mandatory SAC/RMV rate training in the course, SDI does not. SDI will allow you to complete the course with a spare air as a redundant air source, PADI won't.
As far as self-reliance goes. SDI has a major emphasis on this in their training as well. Both courses highlight the same things, with the exception of what I mentioned above. I believe
@tursiops is both a PADI and SDI instructor, so hopefully he'll correct me if I've mischaracterized something.
Personally, how I teach the course is going to depend on a lot of factors. If you have hundreds of dives and I know you, and you know your SAC/RMV, we probably aren't going to do much work there. It all depends on what the student brings to the class. That's the cool part about SDI, you show up "weak" and I'll keep going until I feel you're strong. That's harder to do in the PADI system, if you are meeting minimum requirements, you should get certified. SDI is ok with instructors exercising discretion, PADI not so much.