The quality of your PDF print depends on the original format and obviously the printer. If it was originally done in photoshop, then it possibly was not vector-based and will have aliasing, which can sometimes cause these little dots. It also could be the original settings of the PDF exportation, one or more printer settings, or something with the way your particular printer processes different file types.
PDF is the way to go about 100% of the time as it preserves fonts, vector art and non-aliased printing. TIFF and EPS aren't really used anymore in the field (at least I haven't for over 6 years). 1/2 of my job is graphic design, and 1/2 of that design is print-based, so I'm running into this sort of stuff all the time. You'd be surprised how different printers will handle different formats and how even driver types will affect it (PCL5/6, UFR II, PS). And generally anything printed needs to be created in CMYK format using the CMYK color palate/swatches to preserve proper color processing. RGB conversion usually doesn't pan out well.
You can try importing the PDF into illustrator to see if it has any preserved vector art, then printing it there. If not, you may be able to import it into photoshop at a high DPI setting, adjust, print and see what happens.