I think that it will be impossible to provide the kind of data you want, but we can approximate an answer.
A google search on "Decline of Christianity in Britain" will reveal multiple articles by eminent Britons that agree that Christianity is declining. Lord Carey thinks soAmericans think so. The Telegraph thinks so.
The same search repeated for the USA indicates that the church may not be declining (*Update: I don't intend this single citation to prove the point. I didn't want to base my answer on the simple assertion of OP. While I think OP's assertion is probably correct, I don't have the data and I don't want to gather the data. I started the answer by comparing two google searches - the google search on Britain suggests that there is consensus that the church is declining, while the google search on the USA suggests that the conclusion is still in doubt. I admit that is a very weak methodology, but I think I've made it clear this is an approximate answer.)
How can we explain this? I'm afraid that I cannot list a single, succinct resource, but I think the discussion below relies on Gordon Wood's American Revolution - I have similar information from a bunch of diffuse sources.
In the 17th and 18th century, America was settled by quite a few people explicitly seeking religious freedom (e.g. Pennsylvania, Rhode Island, New England). These people were committed to their faith. They had to be committed, because it required effort to dissent from the national church. Others were non-Christians - Washington's letter to the Synagogue in Rhode Island comes to mind as an example of a non-christian community.
Dissenting Christians in England, and non-christians had a place to go. CoE was the national religion of England. I'm not saying that there weren't devout members of CoE - there certainly were. But if you were English and you didn't care about religion, you were CoE.
Religious Freedom in America meant that you had to choose to believe in a religion, and people did. Sometimes converting multiple times before they found a community and a belief pattern that could accomodate them.
The Great Awakening burned more brightly in the US than in Europe. We were more interested in religious and spiritual matters. I personally believe it is significant that African Americans participated at all levels in the Great Awakening. A free African American could achieve significant status as a skilled preacher.
Political and civic institutions in the US had a different relationship to the church because there was (rather quickly) no established church. The CoE never established a strong presence in the US - as a matter of fact, the last time I was in Williamsburg VA, they were speculating that the absence of CoE clerical positions had a significant effect on the eventual rebellion. That argument is a bit more complicated that I can shoehorn into this answer.
Because the US was pluralistic and immigrant, institutions of affinity played a greater role. In Europe, your identity was fixed by birth. In the US, people had to bind together to form new communities regularly. Institutions like Churches were important for establishing the trust needed for a community.
Essentially, I'm arguing that churches were a more important institution in the lives of early colonists than they were in Europeans. Most of the forces that lead to the decline of the CoE are present in the US, but they are operating against a less committed body of believers.
Pluralism - Because CoE is more monolithic (loosely speaking), pluralism undercuts it more. The USA was designed around religious pluralism.
Modernity. Christianity is designed to appeal to pastoral nomads. It requires some effort to adapt the rituals and scriptures of rural pastoralists to industrial laborers.