It depends on your requirements really and if you're wanting to hook it up to an existing home theatre surround system, for example. It should be pointed out that the standard Dolby Digital and DTS surround soundtracks over optical/coaxial should stilll sound pretty good and because of the extra bandwidth allocated to them would typically sound better than the dvd version anyway.
But otherwise in terms of hook-up to av amp/receiver with the following capabilities;
1) hdmi input able to accept LPCM surround audio - the Panasonic BD35, Sony S550 (or PS3) would provide the best compability with the player doing the decoding. With the S350 you'd lose out on DTS-HD Master Audio decoding which is the lossless audio soundtrack of choice on many Fox movies for example.
2) hdmi input along with in-built hd audio decoding. Either player can bitstream the soundtracks over hdmi for the av amp/receiver to decode.
3) no hdmi input, or input just used for video switching purposes.
a) If it has multi-channel analogue output free, then the Panasonic BD50/55 or Sony S550 would provide the better compatability.
b) no free coaxial digital input, but a spare coaxial digital input - Sony S350 will playback either the standard Dolby Digital surround soundtrack or the DTS one depending on the disk.
c) free optical digital input - either the Sony S350 or Panasonic BD35. However, as you've found the Sony S350 is less expensive and can easily be made multi-region as far as dvd playback. Audio and video quality seem very similiar on both. Again you'd get the standard Dolby Digital or DTS soundtrack depending on the particular disk.
You might find the following
of use as it helps explain the different soundtrack formats present on blu ray and what you need to play them back.