I think that Nippa has/had both of these cameras so would be best placed to directly compare them (assuming he sees this thread, that is).
The Fuji has more DR headroom than the Canon for salvaging highlights, but I find the DR of the Canon hold up well as long as you are careful not to overexpose (it will burn highlights). The Canon has a wonderfuly sharp lens that gives great edge definition. The Fuji is f/2 @ 35mm, whereas the Canon is closer to f/3.5. The Fuji has a nice Fuji colour palette, the Canon has a nice Canon colour palette. The Canon has what I find to be a pleasant noise pattern as you increase ISO, but is probably noisier than the Fuji. The Canon holds up well to processing, but apparently so does the Fuji.
The key difference that I see is not so much that one has better "image quality" than the other, but that the each produce a different type of look to the other and you tend to see each used for different styles of photography. Based on measurable numbers, the Fuji has the better sensor. Based on personal preference, however...that can't predicted or measured. I like them what I see from both of them for different reasons.