I know which is why I think we should consider it based on those constraints.
In my opinion the British Empire wins hands down.
1. It controlled more territory.
2. It did it at a time of multiple large international powers.
3. It had so little resources to start with.
4. Its impact is longer lasting - the spread of English for example.
5. The USA is in fact a product of the British Empire.
The world isnt imperalist or you cant invade countries like before because of UN etc etc so its different.
Most countries UK controlled where empty barren land by weak natives. We know how difficult it was when they faced other europeon powers i.e. napoleonic wars etc etc. Theres a difference between fighting australian natives or africans with bows in 1800s vs fighting a more powerful nation.
I wouldnt say the gap in British Empires peak was bigger than now of USA vs others. I think its much smaller.
Prussia wasnt far off British, or some other powers.
A massive factor against USA is that I think their going to last very short just like the British. I think they peaked already.