It's an interesting question. By having a separate service, it ensured that money for aircraft was spent on aircraft and not syphoned off elsewhere. Yet, the RAF takeover meant many senior RNAS officers were lost to the RN, along with their vision with how the RNAS could progress.
The problem is that the way seniority happened in both the Army and RN experience in aviation wouldn't have counted for much. Progress in the Navy, led to being in charge of a ship, as you get better your ship got bigger!
A continued RNAS which involved aircraft on ships, and a Coastal Command equivalent, might have led to protection of Naval Bases - e.g. Malta.
The RAF OTL descended from 'Air Defence (Gotha Raids), and the Independent Bomber Force (Trenchard's 'baby') - while the original requirement of supporting the Army was ignored as being too dangerous.
I can see with the RN, Light Carriers making an earlier appearance - giving officers an early experience of what it's like to handle a carrier. Torpedo, design would be improved i.e. able to be dropped from a faster aircraft.
With Army Air - I think 'Air Control' in the ME can still happen, but serious planning for a BEF and its Air Component starts earlier, with 'Attack' focused aviation. Heavy long-range bombers may still exist, but on a much smaller scale.
How different could WWW2 go, well the RAF raid on German Naval Bases would be different. Raid carried out by RNAS aircraft - pre-dawn wouldn't have been the fiasco of OTL. While on the Continent, the BEF's aircraft would still be overwhelmed by the Lw - but IMO the timetable of German success would be extended.
What then, after Britain is alone, any 'Bombing campaign' against Germany would take place with a smaller force than OTl, so either have to be more focused and more accurate, or else irrelevant!
Britain has greater success in North Africa, but Germany is freer to wage war against Russia - little interference on the home front.