How important is it to use 4x12 vs 4x8 sheets of drywall?
Its really not important for the end result.  What matters is the workmanship and quality of the installation.  Poorly finished drywall of any size sheet is still poorly finished.  Instead of negotiating a price to install 4x12s, try and find out if they offer a warranty.  My drywaller gives a 1 year guarantee against cracks or sags.  I just get out of his way and let him work, then pay him once I approve the job.  He can use green board, 4x12, 4x8 or 2x2 squares for all I care as long as the finished product looks good and he backs up his work with a guarantee.