The main problem with the Zeiss Ikon is that it doesn't have a large red dot on the front and is further crippled by its "Made in Japan" engraving. These two faults exclude it from serious consideration. In other words, La ilaha illa Allah.
Compared to MP, the built quality for the Zeiss Ikon (ZI) is surely lower, yet beyond adequate and better than current Bessas. The ZI is lighter. Without batteries, the ZI does not work. The MP will. The ZI has higher max shutter and x-sync speeds. The MP has amazing ergonomics and can take a motor drive. It costs $3000 US more. The longer baseline in the ZI is negligibly superior. The finders in both are excellent. The ZI has focal lengths in its framelines in case you're an idiot.
Regarding batteries, the SR44/LR44 required by the ZI for operation are found everywhere. Around the world, I have found these batteries without issue.
I have a ZI, as does a friend. Between the two of us, neither of us have had any problems with ours. I an M6 and said pal has an MP. Neither of us had problems with our Leicas either.
A useful comparison between these two beasts would be
Metal vs. cloth shutter, e.g., sound, durability
Electronic vs. mechanical shutter, e.g., accuracy, durability
For both of which I haven't seen conclusive data suggesting one is better across applications than the other, so I can't really say.
Both are capable of excellent exposures.