To be fair, English/Scottish Enlightenment was also what brought us David Hume and... well, let’s just say that did incalculable damage to faith and even reason at times. So I’m not entirely sure the English/Scottish Enlightenment really differed in that regard. And that’s not getting into how Tom Paine was originally English and a firm adherer to the Enlightenment and was the biggest cheerleader of the French Revolution and its ideals short of Jefferson.
Another great analysis of the whole strand of the enlightenment thinking is the book regarding these by Gertrude Himmelfarb. She sees not two but three strands: American, English/Scottish and then the French with each have their own unique characteristics.
The Roads to Modernity: The British, French, and American Enlightenments