I think OP said: An UK citizen can be extradicted from the UK to the US just by having done a thing that it is illegal in the US but not in the UK.
You said: An US citizen can be charged in the US if he committed a crime abroad even if that thing is not typified as illegal in the US.
Wake me up when an US citizen is extradicted to the UK because he did something perfectly legal in Washington but which is considered a crime in London.