Our background: Wife and I were PADI-certified in the mid-80's. 14-year-old son was PADI-certified in 2004, with me auditing as a refresher. 12-year-old daughter was SSI-certified last year, with my wife auditing as a refresher -- but I read the entire SSI OW manual.
My layperson impressions? Both programs get you to the same point, and it really does depend on the instructor. Others may disagree, and certainly will.
There are minor differences... the SSI curriculum didn't seem to be as structured as PADI's. By that I mean to say that it was sometime difficult to tell, just reading the SSI book, what the skill and knowledge elements were. With PADI, there are chapter summaries with pre-quizzes, as well as sample tests... if you're surprised by
anything on the test, that just means you haven't been doing your homework... and that's a hit on you.
Another example of "structure" was OOA procedures... PADI lays out what procedures to do, and in what priority. SSI doesn't. (I understand that circumstances may require a modification to those standard procedures, by they're good for a beginning student.)
Related to that is my impression that SSI seems a bit more flexible regarding air sharing. PADI at least implies that the "school solution" is to offer the octopus. SSI specifically allows for the option of offering the primary.
Tables are a bit different, with different pressure groups -- which can be a bit confusing. But it's a transferable skill.
Actual table use was stressed and drilled a lot with PADI... there are many different problems on the PADI tests, always including missing surface interval problems that force you to work the tables backwards as well as forwards. I'm not sure how extensively table use is taught or tested under SSI, but SSI is kind of known for de-emphasizing table use. That's also the impression I got from the manual.
Again, I don't think any of these variations makes one of the agencies overall "better" than the other -- but again, some will disagree.
Why do you ask?
Oh... at the end of her SSI training, our daughter had to do a crossover to PADI for her certification dives (the Universal Referral System is a whole 'nuther topic). But I worked through the PADI sample tests with her at home, and she aced the PADI test.
--Marek