The watch that actually was on Buzz Aldrin on the moon had a Cal. 321. That movement was slightly modified (principally in the way in which the chronograph was actuated) and became the 861. The 861 was then rhodium plated by Omega years later and became the 1861, which is what is in the modern, handwind Moonwatch. So, in terms of new watches you can purchase at the boutique, the closest thing you can get in terms of movement to the original Moonwatch is the handwind model with 1861 movement. The other handwind moonwatch has a sapphire (and not hesalite) crystal and is outfitted with an essentially identical 1863 movement that is just a bit better decorated and that has a metal rather than a Delrin (plastic) brake. The upshot is that if you want a brand new "Moonwatch", the closest you can get is the handwind 1861 model with hesalite crystal. I believe the last three digits of the reference number for this model are .001 (on leather strap) and .005 (on bracelet).
