I voted .45, because I have a CavOly .45 ACP carbine which has proven itself reliable and accurate. If I couldn't use the Cavalry Arms MKII lower, or one of the wider well grease gun lowers, I would vote 9mm. This is strictly based on magazines. The grease gun mags work well, but are becoming more expensive. The Colt 9mm mags work well, but are already expensive, (though it seems they might be coming down a little.)
The .40 and the 10mm are handicapped by the lack of good magazines. (Though I understand some people have modified gg mags for both cartridges. I will modify most anything else, but I try to avoid modifying magazines, if I can.)
My experience is that carbine barrels do not slow down bullets from pistol cartridges. Not saying that it has never happened, but I do think that it is a "black swan" event. I admit to almost no experience comparing 16" barrels to 10" barrels, but the one time I did, the carbine still proved superior. In other cases, all carbine barrels out performed pistol barrels with the same cartridges. I still don't have enough samples to mean anything to a statistician, but I am confident that 16" barrels provide higher velocities than 5" barrels.
For those of you who think that the .45 does not improve as much with the longer barrel as the 9mm, I suggest that you look at the kinetic energy increase, rather than the velocity increase. Looked at that way, they come much closer together. Which leads to another point. If you use expanding bullets, you should consider the heaviest holllow points available, regardless of caliber. The velocity increase can cause the lighter bullets to over expand, and under penetrate. That is another reason why I like the .45ACP. It gets that 230 grain up fast enough that it performs well, both expanding and penetrating. At least that has been the case in my semi-scientific experiments.