I'd go for Munich, and staying at the
Deutsche Eiche, smack in the middle of the gay village. There are several bars, clubs etc within walking distance, and the hotel, while straight-friendly, definitely is a gay hotel with a huge bathhouse as part of the complex. Me and my partner have stayed at the hotel several times, and while not luxurious, definitely comfortable. A typical German breakfast is included in the rates, and the restaurant serves good, German meals - mostly to locals. We have not visited the bathhouse (really!) but it is quite famous, and seems to be well patronized also on Sundays. The hotel, it must be stressed, is not in any way sleazy!
I agree that the trip from the airport is quicker in Frankfurt, but the prices quoted are too high - from both airports public transportation is recommended, and taxis at 70 Euros are in my opinion a waste of money. A single ticket on the S-Bahn to the airport costs Euro 9,20 (a single Tageskarte giving free transportation for the rest of the day, until 6AM the next day is only 10 Euros). The most convenient stop in Munich for the gay area (around Gärtnerplatz) is Marienplatz, where the City Hall is, not the Hauptbahnhof. The Airport bus is also excellent in Munich; it stops in Schwabing (convenient for several major hotels there, and the U-bahn) and at Hauptbahnhof. A single is Euros 10,50, return/ round-trip is Euros 17 (bought from driver).