Links are probably the most important factor in every Search engine algo.
IMO, the main differences between search engines lies in weighting factors on anchor text (internal/exteranal), title and heading proximity/density, surrounding text and the refinement of weeding out spam.
Interesting but somewhat speculative question. I think it's mostly a question of having the right links. Only when it's coming to the very huge sites, or sites which just have thousands and thousands of quality backlinks I see a clear advantage - those mostly sit in their #1 slots forever.
But a site with say a dmoz listing, a Yahoo listing and some other baclklinks is in my experience absolutely competitive compared to a site with hundreds of backlinks from all over the web.
Imo FAST has not (so far) put a lot of weight on incoming links. Sure they make a factor but nothing compared to google.
Heini says it; the little guys with a low number of quality links and good optimisation can do just as well as the big guys. On page stuff is important. That's probably why there's a lot of questions like "I'm ranking #1 in Google, but nowhere to be found in FAST".
Well maybe the few high PR guestbook links isen't working for you in FAST ;)