Ps4 pro. Question about Fallout 4 And call of duty

I know question like this have been asked before. But I feel like getting an answer that’s a little more in depth with exactly what I’m asking.

Anyway, No I don’t have a 4K tv. Although I plan on getting one soon. I do have money for the pro. But I’m not full sure if I want it.

See I have this ocd. Where I feel like I won’t fully enjoy the call of duty unless I get the newest version of the ps4.

So how how exactly would it change the way I play? The resolution would be better but would it run better? Almost the home screen of the ps4 lags sometimes. Would that run better as well?

And for fallout 4. Sometimes the game likes to lag a little bit. Especially in the city areas. How does that improve with the new ps4?

And yes I have disposable money for the pro. And I can still trade in my old ps4 as well. I just can’t decide if if laying $300 for this upgrade will really feel like an upgrade.