According to google ngrams the frequency of 'satisfied that' is 0.00026% in British English and 0.00012% in American English. So only a factor of 2 difference.

According to google ngrams the frequency of 'satisfied that' is 0.00026% in British English and 0.00012% in American English. So only a factor of 2 difference. Interestingly the peak of American usage was in the 1860s (~0.001%), followed by a slow decline, but in Britain there was a small peak around 1920 (~0.00127%), then a higher peak in the 1940s (~0.002%), followed by a rapid decline to the present day.