Which brand of digital camera has a better reputation? As many models of digital cameras are cross-brand manufactured (Konica's made by Sony, Olympus made by Richo, etc.) the best thing you can do is narrow your choices down to a few models that have the features you are looking for and then visit a site like http://www.dpreview.com/ where they provide fairly impartial and comprehensive reviews of each of the cameras.
In direct answer to your question, I feel they are a tie. I have seen old Fuji's and Sanyo's that have been through the abuse of extensive travel and are still working today. Fuji has a better reputation as it can be a bit pricy but it is worth it!
hope that helps u | 