Monk/Ranger or Vice Versa?

Is there any real difference between a Monk/Ranger or Ranger/Monk? Do you lose out on anything of value?

Yes, the difference is huge. Start out by reading the sections on Expertise and Divine Favor since that is the major difference.

The other differences are better armor for Ranger Primary and better Energy Regen for Monk Primary.

If you see yourself mostly healing and then getting a few shots in, then Mo/Ra is better. If you see yourself mostly shooting and throwing a heal in once in a while, then Ra/Mo is better. That is all very general though as it is possible to make many builds with Ra/Mo and there are, of course, many special builds possible that would require one or the other combo.

I'm a bit partial to Mo/Ra. Since a healer wants to stay out of the front line, having some marksmanship to plink some arrows in at zero mana cost between heals seems pretty efficient.

Don't forget the fact that being a monk will get you ganked in PvP.