To say that the AA card is 8 times more generous than than the UK one because you get the bonus after spending $250 v £1000 is very disengenuous, quite frankly.

There is a target you are missing. The earnings rate on many UK cards is lower than US cards - take a look at the Hilton or Priority Club cards, for example, and see how many points you get for spending £1k / $2000. The US cards always come out better.

Note also, though, that most UK credit cards have no fee, unlike most US cards. Those free miles need to be paid for somehow!

I would also be surprised if there was any US card that was as generous as the BMI card opening bonus. 20,000 BMI miles is enough for one-way business class flight to the US (with a small co-pay) - is there a US card (especially one with no fee!) that would give you a J one-way flight to Europe as a sign-up bonus?