The question is a little vague and missing much needed context of the shooting circumstance.
Each caliber behaves a little differently and each has certain subtle advantages and disavantages if you are shooting that well. The differences are likely not going to be terribly substantial if what you are talking about is a 1" difference in POI...or so I would think.
With that said, I think what you are looking for is the end result of the shooting. Is a slight difference in accuracy going to make a difference in the fight, right? That is where it gets gray. .45 acp, 9 mm, and .38 special all behave a little more differently. For the 9 and .38, if you are using expanding ammo, they likely aren't going to expand to being much greater in size than the .45 is unexpanced, but they may penetrate deeper. All you can hope for is to land shots where you think they need to land on the outside of the target and hope they continue inward to do the desired damage on tissues you really want to damage. Nobody wants to shoot a person in the center of the forehead, for example. They want a brain shot. Center of chest shots are with the hopes of hitting blood vessels, lungs, heart, etc., not damaging skin in the center of the chest.
The bottom line here is that chances are, 1" or so difference in POI isn't going to make an IOTA of difference in you being able to knowingly hit the internal targets you desire to hit (as in the chest). Heck, the trejectory of your round might be such that it would miss the heart and yet it hits a rib and changes trajectory and goes right into the heart. You can't control that.
I took a class from a guy named Steve Moses here in North Texas who put a phrase name to a concept I like and have felt that make very good sense. People love harping on a slow hit beats a fast miss or as Alan Fud noted, a hit with a .25 beats a miss with a .45. Folks at Thunder Ranch would rather see you shoot slow and make a ragged hole than to have a larger group size. Basically, the concept is that you shoot as fast as you can while landing GOOD hits on target. What is fast and good will be determined by situational context. I feel very comfortable with being able to land 3 hits at 7 yards in a 5-6" pattern quicker than my partner at TR could get off his first shot that landed perfectly in the center. If he were my adversary, I would guess that his delay would not be to his advantage as he would not be able to make that perfectly lined up shot while being impacted by incoming rounds. Given aim and a certain amount of random chance, one of my 3 shots may also be exactly in the center as well. I think I read somewhere about being combat accurate and combat effective. That's all I am talking about. Few have the time and convenience to make sniper shots.
In a hand to hand fight, being able to draw and land shots anywhere on the guy fighting you and doing so very quickly beats the hell out of waiting for the opportunity to bring your little .25 up to shoot him in his right eyeball. You may be dead long before you ever get that chance for that eyeball shot. In contrast, at 25 yards, you have a little time and security to line up a shot (assuming you aren't fighting a guy with a rifle).
In both cases, you want to achieve a 'stop,' whether it is by changing his mind or by incapacitation of some sort. What is good enough shooting to make that happen is going to be quite variable depending on target and circumstance.
I shoot it better than 9mm & there's more room for error.
