They are not double the size of the Wasp-class. The Wasp is 41,000 tons and the QE is 65,000 tons, the disparity in tonnage being easily explained by the existence of the well deck in the first. Dimension wise they are very similar; 253 vice 284 feet long and 32 vice 39 meters abeam at the waterline. As far a physical space they are not that different.
The size of their air complement is not a good metric to use when comparing the size of different purposes vessels. The QE don't have six times the air wing of the Wasp LHD, they both have a normal tactical load out of 40 airframes. However, the Wasp has that ability in addition to half it's internal space being used for Marine ground forces and their equipment.
A better comparison would be the America-class LHA which is 45,000 tons and does not have a well deck
I didn't say double. I said nearly double. The QE is expected to be around 70k given the design changes brought about last October. The 60-65k figure was the STOVL format. Also, I didn't say 6 times the air wing, I said 6 times the combat jet force. IIRC, the Wasps tend to deploy with 6 Harriers.
The QE and Wasp classes are very different ships designed for different roles. The QE class doesn't deserve the accolade of being "the two newcarriers that are barely the size of our LHDs" given their larger size and roles as fleet carriers that carry a similar number of combat jets to the Nimitz class.
Also, the USN and RN have different practices for storing aircraft on carriers, the Royal Navy have always tended to deploy only with the number of aircraft that can fit in the hangar as opposed to the USN who surge aircraft on board, not all being able to fit in the hangars. I have no doubt the QE class could fit a similar number of total aircraft to the Nimitz given the hangar space and deck parking space.
As for the America class, it is capable of carrying around 1700 marines as opposed to the 1300 for the Queen Elizabeth class but it should be remembered that both ships have very different roles and that the primary role of the QE class is not to deliver troops. In the role of assault ship, the America class are evidently better at that as they were designed to be. In the role of fleet carrier, the Queen Elizabeth class are better due to their increased complement of fixed wing combat aircraft. The only jet the America class can operate the slightly less capable VTOL F35B which has lifecycle costs (IIRC) 25% higher than the F35C, according to the British Prime Minister, which can be carried by the Queen Elizabeth class.
A Queen Elizabeth class ship can supply all of Britain's expeditionary air power needs in most conflicts, the less aviation capable America class couldn't and would require either additional ships or land based fighter and tanker support at an additional cost which far exceeds that of the aircraft carriers themselves. Simply put, in the role it was designed for, the Queen Elizabeth class ship is superior to any assault ship. Comparing a fleet carrier and assault ship is apples and oranges really.