First, let me point out that neither the Mark XII nor the Mark XV were one watch. Both were a series of regular and special models. For an excellent discussion, refer to the article by IWC Forum friends Nelson Herring, Hans Goerter, and Adrian van der Meijden at this link:
www.goerter.de/IWCFORUM/MARK%20XII%20SE_English.pdf
Assuming you are considering the two base models, I think the primary differences are movement and case diameter. The Mark XII utilized a JLC movement and measured 36mm, while the Mark XV utilized an ETA 2892 modified by IWC and measured 38mm.
There are many detailed descriptions of each of these watches that you can find using the search function on this site (spyglass icon at upper right) or via Google.
Good luck with your decision. Please post pictures once you have landed your prize.