The simple answer is that it's not answerable. The reason for that is that the way in which crime is recorded in the United States is very different. In particular, there is a category of crimes called “index crimes”, which are the only ones that the FBI collates across large numbers of police departments. We, on the other hand, collect every crime that's reported to the police on a population basis, all police departments contributing.
The decision to go to index crimes in the United States meant that, necessarily, there were fewer being recorded, because it's a subset of offences.
The answer on the one crime where there's easy comparability is on homicides. The United States has typically had about three and a half times as high a homicide rate as we have. It did in the mid-1970s, when in both countries it peaked, and it does now.