Final Cut is Apple's non-linear video editing system. It is used in high end video production by companies including the BBC>

Avid Xpress DV is the company's solution for non-linear editing. Avid Xpress DV's toolset includes professional video editing, effects, audio, titling, compositing, graphics, interoperability and digital delivery tools.

There is a comparison of the two packages here:

http://www.scottsimmons.tv/blog/the-avid-vs-fcp-articles/