I own a 240hz 1080p monitor for gaming, and an 1440p 75hz monitor I intended to keep using for productivity and content. Intended to, but in the end I do everything on the 1080p monitor and the 1440p one is relegated to secondary monitor duties. And I’m using a TN panel. Basically panel technology has come such a long way that the colors and viewing angles on high refresh monitors are not actually a problem unless you’re doing work where color accuracy is critical. And the difference between 1440p and 1080p AT THE SAME SIZE is not that big. Individual pixels are noticeable on the 1080p panel - if you’re specifically looking for them. Personally I’m looking to switch out the 1440p panel for a 4k one around 40 inches - now that I feel would be awesome for productivity.
Now for competitive gaming, you’re not comparing just 240/280hz and 165hz - the resolution also matters, because it will affect your in game FPS. It will be easier to reach higher and more consistent FPS with a 1080p resolution. And it’s not true that you just need to match your monitor refresh rate - even if your monitor only displays 144 or 165 hz having high frame rate in high 200s will absolutely feel smoother.
That said, those are somewhat in the realm of diminishing returns - so in the end it comes down to what is your priority and how obsessed do you want to be about squeezing out the last 10% of potential advantage. It’s not that different from high end audio in that regard.