The biggest single problem with the FAA at the outset of the war CurzonDax was the leadership, only very few commanders had much concept of the potential for carrier based planes or had indeed come from an aviation background (which was fairly normal in the USN)
The battleship was still viewed as the capital vessel and as such the carrier was badly used at first.
For example one commander when asked what he would do if confronted by an enemy fleet replied "steer straight for it", the concept of using the aircraft's long reach while staying out of range of the enemy's guns didn't even cross his mind.
As for aircraft capacity this is a cut and paste from the HMS Illustrious history and explains in fewer and clearer words than I could.
The small number of aircraft carried was due to extensive armouring, including the flight deck. This was considered more important than aircraft capacity when operating close to shore based enemy aircraft. Indomitable's capacity was increased to 48 by completing her with a two-level hangar for half the length of the ship. All went through various war-time reconstructions including a slight increase in deck space, provisions for deck parking of aircraft which increased capacity to 54 and a large increase in AA guns.
This is a list of the aircraft carried by Illustrious during the war
1940: 33 aircraft: Fulmars and Swordfish
September 1942: 21 Martlet, 6 Fulmars, and 18 Swordfish
July 1943: 28 Martlets and 18 Avengers
January 1944: 24 Corsais and 21 Barracudas
May 1944: 24 Corsairs and 18 Avengers
June 1944: 42 Corsairs and 15 Barracudas
November 1944: 36 Corsairs, 15 Avengers
Another factor was that until lessons had been learned regarding launch and recovery of aircraft (mainly from USN advisors ) the slow times that it took the RN too fly off and recover their Squadrons (several minutes greater than that of the USN) meant spending far too long steaming into wind which with a large group of aircraft would place the carrier miles from the battle group.
You are right in your supposition that the Avenger is a larger aircraft than the Swordfish even with the wings folded the Avenger is I believe approximately 29ft wide as opposed the the Stringbags 17ft 3 and nearly a full 4 ft longer.
Although I still believe the Swordfish was the most successful anti shipping plane of WW2 in terms of tonnage sunk there is no doubt that the USN had by far the best carrier based aircraft of the war the few attempts made by the RN to obtain home grown decent fighters, dive bombers etc was not very successful. With a new concept of what carriers could do thanks to Taranto etc and having already adopted ideas from the USN the FAA became a different beast all together and later with planes like the Corsair at their disposal a match for any carrier force.
At the time of the Bismark (May 1941) six months after Taranto it was still however the admirals in charge of the Grand Fleet that ruled the roost besides I do not personally believe the Ark Royal had the fire power to sink the Bismark.
Hope that makes some sense CurzonDax and helps answer your questions
I shall now wait to have my post pulled to bits by all and sundry