Just to add my 5 cents:
I use Tiff with ZIP compression. Takes more time to save, but file size is smaller than PSD and TIFF files without compression.
What is important (for me):
- saving 16bits/channel
- conserving layers
- being able to use PhotoRGB as colour space.
What you need to know:
Editing TIFF files in a different editor than Photoshop will flatten the layers, so be sure in that case to work on a copy, not the original.
A reason for me to use PSD files is, when using the files with InDesign, as InDesign allows me to access the layers in the Photoshop file to switch layer visibility. If you do not use InDesign, there is no need for passing via PSD files. In that case, it's more a matter of preference.
I use JPEG file format only for the final edits I pass on to my customers.