I too have a 2006 Sprint Sunset Red ST. I left my 06 SV1000s for her.
It's not the comparison you were looking for (FZ1 vs Sprint) but here is my comparison between it and the SV:
2006 Gray 996cc to 2006 Sunset Red 1050cc
I recently sold my SV and purchased my new (to me) 2006 Sprint. I haven't logged a whole bunch of miles yet but here is my comparison for those interested.
SV seemed to have more pure raw "umph" down low but the Sprint seems to have more umph at mid-range and higher speeds.
SV has massive engine breaking, the Sprint has a good amount but not as much as the SV
The SV provided me better wind protection (because I put on a extended windshield) than my Sprint (currently rectifying this) which suprised me seeing how the Sprint is a "sport tourer". I catch a lot of wind in the upper chest level at speeds.
The saddle on the SV and the Sprint is basically the same in terms of material used and softness BUT the Sprint kinda "cups" your arse and provides a bit of support higher up your butt so when you punch it you don't slide you just fit.
I've ridden two up with my wife on both bikes - of course there is no comparison here. She definately prefers the Sprint to the SV - but that was what the Sprint was partially designed for so that is no big suprise. The passenger also seems to sit higher on the sprint so it's easier for them to look over your shoulder and see the sights as opposed to seeing the back of the rider's helmet.
GAS! My SV would give me about 120 miles before the fuel light would come on. I usually would ride another 20 miles after that point before I fueled up. (I used one of my trip meters as my psuedo gas-indicator). When I rode to work (45miles one way) I knew that I would have to fill up again soon after a round trip to and from.... The Sprint? Well I can make the round trip twice before needing to fill up. With the SV I think I averaged somewhere around 35mpg, and on the Sprint I am getting 45mpg (basically 200 miles to a tank).
Exhaust note. Well I still had stock pipes on my SV. I have aftermarket pipes on the Sprint. The Sprint definately sounds better, as it should. It's a cross between the twin-sound and the I4 sound.
Overall impression. The SV is raw power. The Sprint is refined performance. Though it may be "heavier" than the SV the Sprint is not lack-luster in the performance category, by no-means! The Sprint suprisingly carries it's extra weight very well. So much so that it feels lighter to me performance wise when I am "getting it in". You can tell that Suzuki cut corners in the parts they used to make the SV (which I just don't understand why they did that) because the overall ride, handling, performance, function and styling of the Sprint is really just on a higher level than that of the SV. IMHO!
But I will always have a special place in my heart for Sally (my SV). For what she cost me she definately proved her worth. She and I both suprised a lot of other riders and their stable-mates when we popped up on the scene. They didn't know who or what we were but when we were done with them...