I previously replied to this post but for some reason it was removed.
If you can, I would recommend test riding both bikes over the usual terrain that you ride. There will be plenty of people singing the praises of both bikes, because both are very good, but ultimately it comes down to personal preference.
I love my Cervelo R3 but have not ridden the Fuji. The bottom bracket stiffness of the R3 is immediately evident as it seems as though that every watt put through the cranks is transferred immediately to the drive chain. A very responsive bike, particularly on the hills. It is also surprisingly comfortable for such a stiff bike, but that is because of the rear stays. I wouldn't hesitate to recommend the R3, but also suggest that you test ride both bikes.
Also check out http://www.roadbikereview.com
for cyclists' opinions, weaknesses and strengths of both bikes.