I've always used PBS (+ tween + milk) and I never ever had problems of background.
I use TBS only if I use primary antibodies against phosphorylated forms of proteins (i.e. phospho form of MAPK); in this case using PBS can give you higher background because of P.
You should use the same blocking buffer system as you have used in other parts of your Western Blotting process. If you are looking at phosphorylated targets or alkaline phosphatase detection, TBS is preferred. TBS blocking reagents are used for detection of phospho-proteins, because the phosphate present in PBS blocking reagents may competitively bind with antibodies to phosphoproteins. I would not recommend using Tween20 in the blocking step, as it is a detergent and may cause more harm than good by creating "deeper" pockets (which causes high background when primary and secondary antibodies get stuck). Depending on the detection method you are using (ECL or fluorescence), I would think twice about using milk, as it results in significant fluorescence.