I digitized a Mini DV tape into my Avid Media Composer and of course it made it into an MXF file and I need to transfer this media from my Avid to My Final Cut Pro system on two seperate computers for two seperate projects.  What is the best way for me to do this with out loosing quality?  Is there a Export setting that I can use?  (I already tried the Quick Time Animation and the file came out WAY to big).

Deaditor

Quicktime DV steam or Quicktime using Apple DV codec

Why not just create an EDL of the material on your Avid and use that in FCP to batch digitise the tape(s) again.  Because you should have already got valid timecodes it should be simple, automated, and painless.