I have not tested the Fuji, so this is kind of a one-sided answer. I have used the Sony, and I can tell you that the focus in low light is very good, maybe as good as my Nikon D70. The grain in high ISO is not nearly as good as a big sensor camera, but unless you are printing 8" x 11", you will not notice the grain at all.
The only thing I have noticed about the Sony is that the colors out of the camera are a little flat. Although many professional photographers prefer the "natural" colors, I like my photos to have more saturation and more "pop". You can fix this in Photoshop, but the Sony files are a little harder to "fix" than files out of MFT cameras like the Olympus EP3 and the high-end OM-D.
For street photograpy, you will be happy with the Sony, as long as you are not expecting it to deliver the exact same quality as a large-sensor DSLR. If you are looking for "Nikon D90" quality or better, I suspect you will have to give up on the small pocket camera.
