PSD is Photoshop's internal file format. It internally carries all the oddball stuff you did to the picture; layers, overlays, texts, alpha, etc. etc, and someone will correct me, it's in Lab format, not conventional RGB or Yuv. It's uncompressed--or compressed in a way that contributes no damage.
TIFF (Tagged Image File Format) is a cross-platform standard uncompressed file format. We use that all the time. You can use LZW (Lempel Ziv Welch) compression with TIFF because LZW does not damage the picture--at all.
This is a close race. Ifyou have an application that speaks Photoshop, use PSD. If not, use TIFF.
TGA (Targa) is another uncompressed format that is widely accepted.
I think the story behind LZW is a scream. Lempel and Ziv developed a lot of compression technologies that didn't particularly work well together. Welch was the one who served coffee and told them that unless they got along, well and correctly, he was going to break all their fingers one at a time.
Koz