On one occasion I did a comparison: UK TA's v US TA's for a specific cruise, in a CC suite.
Whilst I do not recall or have a record of the specifics, I discovered that, whilst — generally-speaking — US TA's will offer more OBC without much discount on price, those in the UK offer discounts on the price but little, if any, extra OBC.
In all - except one - cases, the US TA's provided an overall better deal. UK TA's required less deposit, and final payment was usually a month or so closer to sail date that their US counterparts.
But, the most important discovery was that there was not much difference. The saving I found was never more than 5%.