Sorry I am very late to this party.
I would cast one vote for each! So different, but my favorite two dials among all Lange watches and the most "romantic" pieces in the collection in my opinion. That said, getting an 1815 MP was a higher priority for me and I obtained mine several years before I added an Anniversary. Love them both, but I guess if I had absolutely had to choose, it would be the 1815 Moon.