I use Bricklink more often than PaB and have not had any problems in the 20+ orders so far. Obviously which service you use depends on the specific pieces you are looking for.
I will say that the LEGO Bricks and Pieces service has gotten better, it used to be that you had to wait to get an estimate for your order. Now you see availability and the actual price per piece before you order.
Recently I needed 12 BURP's. Bricklink inventory was limited and expensive. When I checked Bricks and Pieces I was able to get them for a better price than Bricklink. This is generally not the case so it depends on the pieces you need. The one drawback from using LEGO is the shipping time tends to be longer than Bricklink.