Here's an example of something...
Well, how bullet weight effects point of impact. These were shot at 10 yards, single action from a Weaver stance (more or less) using a 4" S&W M681. 6'o'clock hold.
The upper target was shot with S&B 158 gr. TMJ. 14 rds.
The lower 18 rds. of Sig 125 gr. jhp.
(The middle target another gun doing something else. Not relevant here)
If we cut these two groups out and laid them on top of each other (discounting my self induced flyers) you'd see that the center of the two groups is maybe less than 2" from each other. Which is maybe a bit more than I'd get with some other ammo of two different weights from the same gun.
In self defense shooting this would make no significant difference. This is especially the case as I'd be more likely shooting da and fast and moving as whatever I'm shooting at moves.
It would also make little to no difference in many of the combat oriented shooting sports or CAS.
Extend that out to 25 yards and the centers of the two groups would be maybe 3-4" maybe a bit more. At 50 yards an uncomfortable bit more.That difference will vary on the ammo used as well.
To adjust, I could change my point of aim, especially with a favorite load in a favorite fixed sight gun. With adjustable sights, well adjust them.
In some shooting sports like Bullseye or IMSHA and in handgun hunting adjustable sights are a powerfully useful thing. They are also useful in trying out different loads.
With a fixed sight you can choose the load, or cook up one, that does what you want it to do with a particular handgun.
If you choose a gun and load for specific tasks the type of sights on it are a factor to consider. Both types have their strengths.
tipoc