I am a 8 year FO at Delta - I love PBS, much more than Line of Time (LOT) bidding. I wasn't at Delta when they had it, but used LOT at a regional a while ago. The problem with LOT bidding is that you get the good with the bad. For example, a line might have weekends off, but early shows during the week. Or layovers cities you don't like.
When using PBS, you can bid your schedule to be much more of what you want, in the initial award. You want weekends off, trips that don't start before 10am, and you want to get home by 1pm on the 3rd Friday so you can go to your son's All Stars football game? Plug it all in and PBS will try to award it all.
SWA pilots seem to like the ability to add and drop trips, to massage their schedule to get what they want. Well - with PBS, you do that all before the bids come out. You can ask for high time turns, or three days with a DH on the back off it - etc. Our PBS will award you what your seniority can hold. I rarely change my schedule unless I made a mistake and forgot to ask for something off. All that churn in open time is eliminated because everyone is getting what they want - the first time. You don't have to take the good with the bad, you just take what you want. Now if you're junior, you're less likely to get the good stuff, but you'd be surprised what can filter down. Every pilot has different needs for their schedule, one guy's trash is another's treasure.
As Scoop said, PBS is just a tool to implement your contract. At the majors, PBS came about around the same time of the bankruptcy, so our contract was being gutted at the same time. For example, dropping trips that conflict with vacation is a nice feature of your contract at SWA. That could easily be implemented in PBS - we in fact that have for training drops. When you are moving to a new airplane, after training you bid for your schedule. The company designates anywhere from 4-10 days for OE, depending on OE requirements. PBS sees that - but still awards you trips on those days for pay, depending on your requirements, then drops them back into the open time pot. You get still get paid what those trips would pay, but they aren't on your schedule. Similar to vacation drops.
I think the reason that Delta's implementation of PBS works so well is that it (a) honors seniority (I've heard some regional PBS implementations will take a trip from you to give it to a junior guy to complete his schedule and give you a worse trip). Also, the DALPA scheduling group was heavily involved in planning PBS and closely monitors the solutions that PBS puts out, every month. If the scheduling group feels the schedules aren't good enough, it requires the company to tweak some parameters and run it again.