I feel like only Germany is truly making a "conversion", while Japan almost builds another ship from the ground up, except using the hull itself to make up for their lack of steel...
Plus, I would like to argue a little about the aircraft capacity for the German carrier design. (I know, the two are designed for completely different purposes, and faces completely different situations, but I'm doing it just for fun)
The show credited Japan for two advantages: air wing size, and take off methods.
However, I would argue that despite a smaller air group complement, the German carrier's aircrafts are much more powerful. First, the fighters.
Boasting a heavier take-off weight, better power to weight ratio, high altitude performance and speed in all altitude and situations, the Germans with their Bf-109 can quite easily assure its air superiority despite the numerical disadvantage.
The German strike aircraft, the Stukas, share similar advantages like the fighters, but most importantly, the Stukas are much more flexible. The IJN Nakajima B5N can carry 800kg high explosive or armor piercing, but they would be absolutely useless in a surface engagement since the airframe cannot withstand divebombing stress and can only be dropped from a horizontal high altitude run. The Stuka, however, can deliver both bomb and torpedo payloads to the enemy. Another thing to be noted is that on board Shinyo, the Nakajima might not even be capable of carrying a full payload due to the shortened flight deck compared to the larger carriers like Akagi and Kaga, on which it takes the whole length of the deck for the Nakajima to take off with a full load.
Yes, the German design requires the use of a catapult, so what? As a commerce raider, the 16 plane launch capacity is well enough to be successful. In need of a fighter scramble, the catapults are capable of launching the entire fighter squadrons in the sky. In a surface engagement scenario, the hanger can be emptied of its Stukas, plus 4 fighters for patrol and reconnaissance.