The idea for the RN in terms of carrier aviation is that while it is nice to have CATOBAR it is an expensive option - aircrew training and rotation plus attrition on the airframes is much higher than for the STOVL and the RN has won at least one war with STOVL. I understand that one estimate was that you would need something like 80 F-35Cs plus a load of T-45Cs or similar to put out the air wing that can be achieved with a fraction of that with F-35Bs that can be qualified for carriers in a fraction of the time and effort.
In terms of the capability of the F-35B (and I will keep this brief), with STOVL as opposed to "true" VTOL the amount of weight that can be taken off with and brought back is much higher. I suspect the USMC may, if the USN doesn't do this spontaneously, start to build ski ramps on the various LHAs and LHDs.
The other element(s) to consider are that the QE class of carriers are built to be the centre of an amphibious expeditionary capability and CATOBAR would take up a lot more deck space and upper levels to do, which on the QEs is used for storing Royal Marine Commandos and helicopters.
Last, but not least, a CATOBAR QE would need to either have used the electro-magnetic catapult still rather new as a technology or have some sort of hybrid steam generator as they don't run on steam otherwise.
