The subject of air to air gunnery (as opposed to the subject of the guns) is a woefully under studied one.
I don't believe that any nations (people) were any better or any worse shots than any other.
What differed was
Instruction and
Practice. The
Quality of both and the
Time spent on both. These varied considerably throughout war in just about every Air Force (or every Air Force?). Let alone from air force to air force.
For example For the US you had John Thach, " graduated from the
United States Naval Academy in 1927 and spent two years serving in
battleships, before becoming a Naval Aviator in early 1930.
[2] Thach spent the next decade serving as a
test pilot and instructor and establishing a reputation as an expert in aerial gunnery"
another source says that during part of that time he was a gunnery instructor. Please note that he had been flying for 12 years at the time of Midway.
"In the early 1940s, he was placed in command of
Fighting Squadron Three (VF-3). There he met a young
ensign just out of flight school,
Edward O'Hare, later a
Medal of Honor recipient. Thach made O'Hare his
wingman and taught him everything he knew. At the U.S. Navy fleet gunnery competition at the end of 1940, eight of the 16 VF-3 pilots qualified for the gunnery "E" award ("excellence")"
See:
Butch O'Hare and the Thach Weave | U.S. Naval Institute
For an interesting story about Thach and Butch O'Hare.
Unfortunately for the british, it seems to an outsider, that too much of the 30s was spent on NEW theories (no allowance shooting/turrets, aiming fixed guns in multiple directions) ) and not enough on getting the most out of what they had. Gunnery training
seems to have been done on once a year (?)
camps where the squadrons left their home fields and operated out of the gunnery (or bombing) field/base for one or two weeks. I could be wrong about this but this is hardly the way to reach high standards of proficiency. I would note that Thach was probably an exception to the rule of how the USN was operating/training at the time.
The Boffins can invent all the fancy sights they want (not to disparage the Boffins, better equipment is always useful) but if time is not given to training and practice then the improvements in equipment are never up to what they could be.