That has been discussed indepth before renrich. The saviour of the British Isles in 1940 was the English Channel and RAF. The Royal Navy did not need to partcipate because the Royal Air Force deprived Germany of the air support.
In my opinion there are only two air forces that could be in the running for number one spot; that would be the USAAF and RAF. Even disregarding the actions of these two forces they provide the framework for a well-rounded, well-organised air force.
Both the USAAF and RAF had tactical and strategic force in mind. This generated effective ground support for troops and devestating strategic bombardment. No other air force provided strategic arms like these two did and, in fact, no other air force except the Luftwaffe provided tactical organisation on the level of the 9th US Air Force and 2nd Tactical Air Force.
Taking the tactical side alone the USAAF and RAF provided much better support to their troops than any other air force. And could operate in the battlefield for a longer time due to the two party movement system with the battlelines. The Luftwaffe never did this so when a group moved, it would all have to move which took it out of the battle for a few, maybe crucial, days.
No other air force had the organisation of these tactical forces. The Ninth Air Force, as well as 2nd TAF, were organised in a manner that left them seperate from any strategic attacks on the enemy. Given transport, light bombers, medium bombers, fighter-bombers and fighters these units were from one command that co-ordinated the operations to near perfection.
While the tactical side offered pure tactical support, the strategic arm of these forces act seperately but with equal skill and determination. It is this strategic arm that no other air force could match. Without the heavy bombers with doctrine, organisation and fighter escort to support - no other air force could be recommended for No.1.
The logistics provided to both these forces was immense and amazing. Both countries kept their forces supplied throughout the globe from Duxford to Ramat David to Rangoon. From Los Angeles to Kiska to Iwo Jima.
No other air force could do this. No other air force rounded itself to the task of strategic and tactical support, no other air force operated in every task in every theatre.
So, it's close between them both. But I have to vote for the USAAF because while it was behind the RAF in 1939 - overall it achieved something the RAF never did. The USAAF operated both tactical and strategic arms in every theatre it was fighting in, the RAF only operated tactically except in North-West Europe.