10^12 is british
10^9 is american
The british one has fallen out of favour a bit because its a bit to big the be used that often
However... if you think about it the British one is more logical because it means you're making full use of your numbers and you're using a system in which it's obvious when the next name for a number will come up.
What do I mean by this.... well when we get to thousands we then go up through all our existing numbers to describe the amount of thousands.... up to 9 hundred and ninety nine thousand 9 hundred and ninety nine, then we need a new number: a million.
So.... The efficient thing to do would be to 'use up' all our numbers to describe how many millions we have before introducing a new name. Hence we'd get up to 999,999,999,999 or 'nine hundred and ninetry nine thousand nine hundred and ninety nine Million, nine hundred and ninety nine thousand, nine hundred and ninety nine'
.... and then we'd need a new number.... One billion
That said, beyond that point the british system is just as bad because Trillions, Quadrillions, Quintillions, Sextillions etc. are all just a million times the previous one