I dont recall all of the differences but I know that I chose the S550 because it had analogue out for HDaudio (I have an old amp that couldnt receive or decode audio via HDMI) and it is also profile 2.0 out of the box, if that is relevant. the S350 can, I believe, be updated to be profile 2.0.
I believe the picture quality was regarded as being the same. If you are getting a new AV receiver then having a blu-ray player that can decode and send HD audio via analogue might not be important to you.
The price is another difference
There are new Sony's due out soon-ish if you wanted the latest versions