If cumulative happiness over your life is the goal then the first one is clearly the wrong approach. The probability that you will die/become incapacitated/have health issues before you can either build up or enjoy for a long period of time that F-U money puts a discount on the entire end state.
No, memories accumulate. And in my very normal and apparently common experience, rose colored glasses and "I earned my success by struggling" make up for any past lack of happiness I've experienced. Those memories are white-washed unless you've had some severe trauma.
So the only thing that really matters is if you currently happy, or if you are about to become happy. Nothing accumulates.
If you're the kind of person that likes to go up the ladder, every step up provides you with happiness so I don't think your story is a counter example.
On the one hand you have the people who give 100% of their day to work, with the goal of building up F-U money and never working again.
On the other hand you have the people who make less & save less and plan on working longer, but take more of their day for themselves.
I don't think I can say either philosophy is wrong, but they definitely don't see eye-to-eye. They have different value systems.