Pucka, every airport has it's unique elements, but to say that a US controller would have difficulty adjusting to how busy Heathrow is, well that's just something I don't buy.
As I said this is by aircraft movements.
CLT was comparable until they added the third runway in 2010 it has an additional long parallel runway. LAS is also comparable. The busier airports like ATL, ORD, JFK, etc. all have more runways simply because they need them to handle the volume of traffic. LHR would need to almost double it's traffic to approach ATL.
I also don't think LHR controllers would have much difficulty going the other way.