The arguments for Nuclear have been discussed at this point, things such as being able to run for a long time without refuel or having more aviation fuel.
But just talking about why A is better than B misses the whole point that maybe its better in peace time fighting against weak opponents, it might not be optimal strategically against another superpower fighting a total war.
German Panzer or Tiger tanks were bigger and technically superior in every way, but they were a strategic failure compared soviet T-34. Soviets correctly understood that a tank has survivability of just a couple days in the battlefield and doesn't need all these fancy things. It just needs to perform a few missions well and quality will be compensated by the ability to mass produce the tank and also ease of maintenance. T-34 was mass in the 100s of thousands compared to a few thousand German premium tanks and germans ultimately suffered because of it. They failed to grasp the strategic nature of warfare.
Just because US uses nuclear carriers when it faced no peer opponents for the last 30 years doesn't mean China should or will follow the same strategy. China has a different regional landscape and different strategic needs.
China faces pro-US countries like Japan, Korea, Philippines or even distant opponents like India. US itself is also likely to join any war. So, it faces an opponent that will have very sophisticated anti-ship missiles. Essentially they will apply A2/AD carrier killer strategy against China. In this kind of threat environment, the chances of a carrier being able to survive and also be useful in battle could be quite limited. Maybe multiple carrier could be lost in a single battle in a war China is likely to fight.
So, I don't think having the ability to run for 20 years non-stop or carrying more aviation fuel is all that important when the carrier may have a lifetime of just weeks in a real fight. It might be more important to have smaller but more numerous carriers that can spread out the air cover more. It might be more useful to have cheaper, more maintenable or more numerous Carriers compared to having a few extremely expensive nuclear carriers which must be protected at all costs with too much resources. Distributed lethality is the buzzword nowadays.
In fact, even having carriers could be obsolete in the modern battlefield when air-defense and anti-ship missile tech has advanced so much. Maybe the future of naval battle is drones carriers and missiles. So, I don't think China having a nuclear carrier based Navy is a done deal as some people here are saying.
I think China could just build a few carriers just to have another option during wartime and show the flag in peace time. But the primary arsenal of the navy could be its destroyers or drone carriers. I think future naval battle is changing and assuming 30 year old US strategy is still useful or applicable to China is dangerous.
