A perfect example of differing naval doctrine was the USSR and the US. The US' surface heavy hitters were its aircraft carriers, long range, heavy and powerful catapult launched strike fighters off of high endurance carriers. They were the prime movers.
Whereas the Soviet Union had a naval doctrine where their aircraft carriers were purely air defence assets to support their missile carrying cruisers and submarine force. Their aircraft carriers carried some extremely heavy SSMs themselves. Their carrier was using STOBAR tech as their aircraft only needed an air defence loadout as opposed to being loaded down with PGMs, AShMs and huge amounts of fuel for long range strike.
With respect to the UK and France, the different choice of aircraft carrier technology comes into several topics
Firstly when Europe was looking for their next fighter, France wanted a multirole fighter capable of catapult launches from their aircraft carriers, IIRC it was around the mid 80's when France splintered off and began the Rafale fighter program. At that time, the French had a pair of conventional Clemenceau class aircraft carriers, whereas the UK decommissioned our own conventional carrier in 1979 and the program to replace that class being killed in 1966.
So when the Rafale was born in the mid 80's, the French had 2 CATOBAR carriers in operation whereas the UK had 3 Invincible class aircraft carriers which were STOVL flying Harriers from them. We've been flying STOVL missions for 3 decades excusing the recent hiatus. It's pretty much become the way we do things and it's not actually a bad way of doing it.
When this carried over to our current carriers, they were initially designed for STOVL operations for a number of reasons but had the redundancy built into them to have EMALS and AAG installed further in the ships life, but these design elements appear not to have ultimately made it in which is why it became hugely expensive to retrofit to our second carrier.
Different methods of flight operations but the same barebones goal; carrier based power projection.
With respect to propulsion, that's a financial decision based on capital cost, R&D cost on designing the reactor and rolling in sustainment cost over the lifetime of the platform. We found conventional more suitable to our needs, the French wanted nuclear and put a pair of sub reactors in for their propulsion with mixed results.
EDIT: Hopefully my dates are accurate.