Well that's a somewhat difficult question
Some of the differences I see are basically that PADI instructors cannot step away from the "formula" they are told to teach, nothing less and nothing more, the PADI system works just fine and for what I know the majority of divers today dive using what they learned in their PADI courses and are doing just fine so there's not a problem at all with that, the problem I see in their system is that "formula" in wich the "PADI way" is the only way taught. I don't like that, another thing I don't like is that divers can go straight out from the OW course to the AOW and that doesn't seem right to me.
SSI instructors as well as NAUI instructors can change somewhat the education they give, never take from it but actually add to it, in my case I asked my instructor if we could spend some more time practicing in my buoyancy underwater and we are going to, he offered to take some time appart with me so he can explain some of the phisiological aspects of diving in depth with me (since he saw I was very interested in learning more about that), also the way in wich SSI teach procedures I find better not the procedures by themselvbes but the fact that PADI divers only do stuff once or twice and then the class moves to the next topic, SSI makes you practice until the movement happens in a somewhat second nature way, also if you want to go AOW you need to have at least 24 dives logged (including the dives from the AOW course), of course any PADI shop will take you as soon as you get your SSI OW and make you into AOW but you won't get that in SSI, 24 dives no less this puts an emphasys in experience wich I like very much.
These are just examples that I can extrapolate into what I think/feel is the "attitude" of an agency, maybe I am terribly wrong but it makes sense to me.
Oh another thing, I feel the PADI tables are way too liberal, not saying they don't work or are faulted just seems too liberal for my taste.
I am not in ANY way trying to say PADI is not a good agency and I like a lot of things about them, they just don't suit my taste in some things and SSI does so I go SSI, for some people PADI may adapt better to them for me is SSI.