I think you've got it the wrong way round, actually. British shows typically run for a 6 episode series and then might go several years before a new series is produced. The Thick Of It has had 24 episodes since its inception in 2005, whereas its US adaption has already had 28 since 2012. Armando Ianucci (the writer) has straight up stated that he won't write any more The Thick Of It until he feels he has material worthy of new episodes.

I think it's the US networks putting pressure on writers to produce produce produce which ends up being the difference between the perfection of The Thick Of It and the greatness of Veep (in my opinion).