Both formats use lossless compression, but TIFF offers the additional option of ZIP compression. However, ZIP is very slow and may not save more space for some file configurations. PSD has some definite advantages if you work with other Adobe applications. For example, Adobe InDesign can control...
I started using TIFF after doing a course in Brighton at Garage Studios. After they explained the advantages over a PSD now everything I shoot in RAW is exported as 16bit TIFF for post work. I convert down to jpeg for posting online, or for sending to magazines/agenci...
It has no advantages and many disadvantages over TIFF. TIFF is publicly documented, PSD is not. That makes TIFF a preferred file format for the long term conservation of digital files. TIFF uses ZIP compression for max compression, PSD uses RLE which if you save without the Max compatibility...