As I recall the Luftwaffe code, I think it was called "Red One" was less secure then the others and was read fairly consistently by the British during the war, although as I recall from Blair (it has been a few years since I read it) this had more to do with lax procedures on the part of Luftwaffe operators than a problem with their Enigma machine. Breaking the Luftwaffe code was a major break since it gave the British insights in what to look for in breaking the other German codes.
The Germans were also able to frequently break most British naval codes and to decipher a lot of stuff in 39-42.
The big difference is that the British knew their codes were vulnerable and were always changing them and tightening their security procedures while the Germans were convinced that Enigma was unbreakable, which turned out to be their weak point.
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