TIFF was used for print back in the day before jpegs could support CMYK color with variable levels of compression. I find no reason to use TIFF anymore (TIFF can also preserve layers, which might be useful for sending files between PS and gimp?). Not sure, I dont use gimp so i havent tested that. Either way, a PDF can do everything a TIFF can + more.
As far as saving the most efficient flattened file, if working with a file that is going to be printed massive and viewed close (best quality), I'd work in CMYK color and save a flat version of my PSD as a PDF. Otherwise, there is no real reason NOT to save something flat as a jpeg (or PNG).
The benefit of using a PDF is that it's viewable by pretty much everyone, but can preserve vectors and photoshop layers potentially if someone reopens it with PS.
Maybe I am forgetting something...?