Are they sync speeds from your router or the results of a speed test?
It's unlikely that your sync speed will change as this is governed by the quality and length of your phone line and, as such, is something outwith your ISPs control.
If it's throughput - it will depend on how congested PN's network is compared to BT's as well as being dependent upon any contention at your exchange. PN have just added more capacity to their network, and have been regularly adding capcity over the past couple of months, to keep ahead of demand so I'd guess that you will probably get the same or better speed with PN.
plusnet BBYW Option2