At DAL we have had NavTech for a year now, and I know very very few pilots who would rather go back to Line of Time bidding (although to be fair we get serious headaches over the months of Nov and Dec). The key is: you MUST have an agreement with the company allowing for union oversight of the bid award process, and you must have a good education process prior to going "live" with PBS. If you don't you are just opening up a huge hole that the company could throw you through.
NavTech's system is so far superior to the line of time system we used to have that I could spend a long time just detailing why. Suffice it to say that I had to go through all sorts of hoops with the line bidding, plus all the "after the bid" adjustments we used to do, just to get a worse result than I get on my first try with PBS. I am middle of the pack seniority-wise also.
Last, I have never understood why the same pilots who don't trust most management in most issues don't have a problem with their mgmt side of the house determining what lines they could bid on, when there are limitless possibilities.
The key is always have the union be an integral part of the PBS vendor selection, education, and implementation process.