Also which one of them had overall superior Anti Air performance ?
The Richelieus' 380mm turrets were very different in design from the 14in turrets on the King George Vs. The Richelieus' turrets were divided into two separate compartments by a fireproof bulkhead, with two guns in each. This reduced the likelihood that all four guns would be knocked out by a single hit to the turret. The quadruple turrets on the KGVs were not subdivided. This difference can be seen from the outside; the Richelieus have their guns mounted in two groups of two with a larger gap between them, while the KGVs have theirs equally spaced. The KGVs had a vertical face to their turrets. This gave better protection against fire at long range, but made balancing the guns more difficult. It also left part of the barbette structure uncovered by the turret, which had to be protected by an additional armour plate. The Richelieus had a more conventional sloped faceplate. This was somewhat worse against fire at long ranges, but reduced the size of the holes in the turret roofs and made the guns easier to balance. Beyond the external features, the means for loading the guns were very different. The KGVs used a conventional loading system. To load the guns, they had to be lowered (or raised) to an angle of 5^o. At this angle, the shell was rammed, then the two charges. The French used a semi-flexible rammer, which theoretically allowed for loading at any angle. As the French system did not require the guns to be lowered and raised after each shot, it theoretically allowed for a higher rate of fire, with a 25 second loading cycle compared to 30 seconds for the KGV's smaller guns. In practice, though, the French could not use this high rate of fire. The hoists on the Richelieus were slow and unreliable. During gunnery trials, Richelieu fired one salvo every 80 seconds; while engaging the British at Dakar, she fired once every two minutes. Post-war modifications allowed them to fire every 32-40 seconds. The British also suffered from loading problems. The shell rings (shells were transferred from the magazine onto the shell ring before being hoisted into the turret, allowing loading at any angle of train) had too high tolerances. As the ship moved and flexed about them, they had a tendency to jam - this put King George V's A turret out of action for half an hour during the Bismarck action. There were also problems with the interlocks used to ensure flash-tightness.
As far as their anti-aircraft performance goes, I'll compare the ships as designed. Different ships from the classes had very different reconstructions at different times, making fair comparisons difficult. The anti-aircraft battery for a warship in this period can be divided into a long-range battery and a close-range battery. The long-range battery on the Richelieus consisted of fifteen 152mm guns, in five triple turrets. The KGVs had sixteen 5.25in (133mm) guns, in eight twin turrets. Both were dual-purpose weapons, capable of engaging both surface and air targets. The French battery may seem heavier - the guns are larger, and the design can bring nine barrels to bear on a target on either beam, while the British can only bring eight to bear. However, this is illusory. The guns and turrets were too large to train and elevate quickly enough to track fast-moving aircraft. They had a complex hoist system, which lowered their rate of fire to five rounds per minute in the AA role from a planned eight. The British guns had fewer problems, but were still not ideal. The turrets were too cramped, and the shells too heavy for easy manual loading. Even so, they could make seven to eight rounds per minute. Their rates of train and elevation were faster than the French turrets, but still not ideal, especially if power to the turrets was knocked out. In terms of their close-in batteries, the French ships had six twin mounts for 37mm guns, and six quadruple mounts for 13.2mm machine guns. The 37mm guns were semi-automatic weapons, with a low rate of fire of 15-21 rounds per minute. This made it all but useless as an AA weapon. The 13.2mm machine guns had a high rate of fire, but they were only useful at close range. Additionally, their bullets were too small to do much damage. The British had four octuple mounts for the 2pdr 'pom-pom', a 40mm weapon. This was a fully automatic weapon, capable of firing at a rate of 115 rounds per minute. It fired a heavier shell than either of the French weapons, and while its muzzle velocity was somewhat low, it was useful as an AA weapon throughout the war. King George V and Prince of Wales also completed with launchers for the Unrotated Projectile AA rocket (4 in King George V, three in Prince of Wales). This was a useless weapon, and was never fired in action. Even so, the 'pom-pom' gave the KGVs a far superior AA battery to their French counterparts. This was especially true due to the layout of the weapons. The all-forward design of the Richelieus meant their secondary battery and AA weapons were concentrated aft, making it harder to engage aircraft approaching from ahead. The conventional design of the KGVs gave better all-round fire.