I think there is definitely something wrong with the comparison. F10 was tested by Simon as having resolution surpass all 7MPs, and rivals to his quality benchmark - 8MP Oly 8080. It is very doubtful that S2, being the 5MPer, will be any exception.
You shall post the original F10 pics with EXIF intacts so that we can understand better. It looks to me that the F10 shots all aren't in focus and being overexposed badly. And then, comparing ISO200 vs ISO50 is not scientific enough.
I have a F10 too , and to my surprise it's crispness and sharpness easily beat my FZ20, easily visible in 100% crop. Again, FZ20 has slight lead in quality to S2, this just adds more doubt to me.