The Germans were quite successful in their code cracking actually. The Allies lacked a machine as sophisticated and frankly impressive as the German Enigma.

The Americans refused to allow the British to use their ECM Mark I devices, so the two groups weren't even using the same code or encryption devices. British operatives and resistance fighters used a couple encryption devices including the Paraset, but there was no standard system like Enigma in place for all the Allies.

However, the British and Americans were also slow to change their code systems. German forces had cracked the British Admiralty's code back in the 1930s and the British Navy didn't have a truly sophisticated encryption system in place until 1943. Before that German groups were able to crack two versions of the British naval codes and as such knew the positions of British ships throughout the Atlantic. The same was true of the Americans until 1942.

BUT the Germans did not have a centralized force assigned to the task of deciphering codes like the British did at Bletchley Park. As a result, there was overlap and wastefulness in their efforts that a coordinated approach may have avoided.

Also, even when a transmission could be intercepted and deciphered, something like 90% of the time it wasn't until after the information was obsolete or an event had already happened. I'm not an expert by any means, this is just what I remember from a very long WWII spy phase a few years ago. If you're still interested, I recommend reading The Man Called Intrepid by William Stevenson. He does a great job analyzing the SOE's GC&CS's efforts to decode Enigma etc.

In the pacific theater initially the SIGABA machines were used but these proved too time consuming in the fast moving battles on small islands. As a result the Navajo code talkers were used. Essentially they spoke their native language which was almost entirely impenetrable to anyone who had not made an extensive study of the dialect (something to do with how verbs are conjugated I believe). The words of their language weren't enough (There is no Navajo word for aircraft carrier for instance) so a dictionary was intorduced that contained a phonetic alphabet as well as equivalent Navajo words for those commony used in battle. Planes were named after different types of bird, boat after sea creature etc. There were also code names for countries (Iron Hat for Germany, Bounded by water for Britain etc). When asked after the war the Japanese admitted to having broken SIGABA but they could not even transcribe let alone break the Navajo code.

With relation to the Germans, when I visited Bletchley Park (so this may be fairly romanticized) I was told that the Germans had many disconnected code braking services who were all in bitter rivalry with each other. I was told that there were fights in the street between members of the different group. This is repeated in Simon Singh's the code book through I'm not entirely convinced of it's accuracy.

If you want to read more about codes in General then The Code Book is a very good read although it contains Mathematics in equal measure to it's history so be warned.