Well, I'm not good enough shooter and I haven't shot enough similar guns in 38 Super vs 45 to say if one is still inheirantly more accurate than the other. I can't consistantly hold 2" groups at 25 yards in any unsupported hold so, most properly fitted semi customs (Rock Rivers, Baers) are more accurate than I am.
In Bullseye, with the 45 (or any larger caliber) with certain placements, you are slightly more likely to cut into the next ring so indentical shooters with indentically accurate guns and indentically accurate loads will eventually have a higher score with a 45 than with a 38 Super but with all being identical and standard group measuring, they should still be the same. But in most competitions, you want every advantage you can get.
Of course, in some compeitions, faster shooting is more desirable and most have found that the 38 Super or very light 9x23s result in faster times while staying on target than 45s.
Having said both of those things, a 1911 in either is far better than no 1911. If you want it primarily for gaming, I might suggest you look closely at the 38 Super. If you want it for a carry piece that you will also use in competition, I'd still lean towards the 45. Either way, since you reload, the costs will be kept down... It will still be cheaper to reload for the 38 Super than the 45ACP.