PBS is Phosphate Buffered Saline which is PH 7.4 and usually used in cell culture, TBS is Tris-Hcl Buffered Saline which is PH7.5. When used in western-bloting, add 1‰ tween-20 to the buffers and the both have similar function, you may use either buffer for antibody dilution and membrane washing. But when your primary antibody is phosphorylation, you may use TBST nor PBST. Personal perspective, PBS has a phosphate anion may disturb the phosphorylation antibody detection. I wish it helps.
Everything covered above, but just to clarify in general: avoid PBS in any method that is sensitive to the presence of phosphates. Avoid TBS in any method that is sensitive to the presence amines.
Also, the phosphate of PBS is more stable in terms of pH vs. temperature than TBS, if you are doing your blocking elsewhere than ambient temperature.