Sorry, I did not know you were talking about the transparent shadow. DPI and opacity will have a lot to do with that, I normally make the image with the drop shadow much bigger then apply the drop shadow. The scale it back down to the original size, you get a better effect and control of the shadow.
To make sure it prints correctly you will need to flatten the entire image, or make sure your dithering types are the same. You're gonna have to experiment with that a bit depending on your printer and profile.