British and Americans have all of these amazing/known programs of codebreaking and the Soviet NKVD seemed to be able to slip a spy into anything. The Allies also became very good in military diversion/"maskerovka". Their sophistication and creativity in deceiving the Axis seems limitless, at least based on popular stories.
On the other hand, the Axis seemed to have failed in their intelligence gathering, over and over. Greatly underestimating the strength of the Red Army, inability to determine the location of allied landings, and other intelligence disasters, like giving up the exact timing of Operation Citadel.
I get that beyond the ability to work with various resistance groups and partisans in occupied lands probably benefited the Allies greatly in intelligence gathering in occupied lands, but there were plenty of Nazi sympathizers in those areas too. There were many right leaning people in western Europe and plenty of anti-Semites in Belorussia and Ukraine, for example, who were nazi collaborators.
What's the story of Axis intelligence?
I can recommend the book "The code breakers" by David Kahn. According to this book which talk at length on german code breaking during WWII, the nature of the nazi government was to encourage competition meant that there a was a lot of double work. Abwehr and the gestapo didn't cooperate of cracking codes. The other was the idea that enigma was unbreakable. It stands to reason that if Germany had made an unbreakable encryption machine, the allies must have done the same, thus trying to break allied code was futile.
Should be noted that in this book a point is made that the head of Abwehr, Admiral Canaris, who was a hard anti-nazi and ran a resistance ring inside Abwehr decided to inform the Vatican about the holocaust. As Abwehr had cracked the vatican codes he made sure this information was delivered by currier to the Vatican. (Details can also to be found in the Nurnberg trial transcripts).
"The codebreaker" is rather pricey, but it's one of the most well spent money I ever spent. It deals not only on German but go into great details on allied code breaking efforts. Giving a nice comparison.