PS3 has wi-fi in-built. Plus, its own hard disk which can be upgraded. PS3 also gets frequent firmware updates. 3D has been enabled in PS3 with a recent firmware update (version 3.50). Not to mention, PS3 was the first blu-ray player, and for a long time, was the best blu-ray player around, till other players like Oppo came in.
Processing-wise, I do not think there would be a great amount of difference between PS3 and BDP-S370. Both, however, will be region locked to blu-ray region C. I am not aware of any methods to make them region-free.
All in all, there are few advantages of PS3 over S370 as mentioned above. If you'll be using ONLY blu-ray playback (non-3D), then both are good. However, if you'll be needing gaming or other PS3 specific features (wi-fi, 3D), then PS3 would be a better choice. Not to mention, the PS3 looks smarter.
Note, however, that you would need to purchase the PS3 BD Remote separately if you'll be doing a lot of blu-ray playback. Getting used to the game controller for blu-ray watching will be a bit cumbersome.