Any number of reasons come to mind for why the group size would open up, but of course they are all just possibilities.
1) Grip angle and feel. (I'm assuming you weren't shooting off a rest). Impact varies based on shooter and handgun.
2) Familiarity. Impact varies based on shooter and handgun.
3) Ammo consistency. Matters, but at 10-15y quality ammo will have a real but not huge impact.
4) Tolerances and wear of the pistols in question. I'm not familiar enough with the weapons in question to comment on how much impact this will have.
and...my best guess:
5) Sights. Obviously this will have a huge impact, not only quality and visibility vs target, but also the style. 3 dot vs notch and post vs high viz, etc. How much light is on either side of the front post matters for accuracy. Look at target shooting sights vs combat sights. The first will have narrower gaps on the sides of the front post when the irons are lined up, which makes for more accurate shooting. More combat oriented sights will have a wider gap, costing some accuracy but increasing the speed and which you find and align the front sight in the rear notch.
I'd say some, or all, of the above would account for it more than the physics of the round at the ranges we are discussing.
Like Vic said, there are .380 gun/ammo/shooter combinations out there that group very well.
When you get to the competition level in terms of gear, ammo, and skill, then the physics of the round (and the rules of the game) will start to make a difference. A tiny difference, compared to the rest of what I've already covered, but a real one when you are shooting 1.5" groups at 50y. Not so real when you're shooting combat drills with carry equipment and bulk ammo at 10-25y, regardless of skill level.
It was definitely shooting fundamentals/familiarity involved. The LCP has almost no sights. I buried the target with the nub and held on tight, but not tight enough to let the little bugger control my hands. I was honestly sucked I hit the plate the first time lol. Now if I could just learn to curve bullets like in the movie Wanted I'd be in business!