I don’t really have a “dog in this fight” and haven’t performed any tests with either .30C ball or .38spl ball, but I would suspect a valid analogy would be .22LR vs .223 or even 223-vs-.223subsonic.
The 5.56 55-grain fmj is a very good anti-personnel round, but the same bullet at .22lr or .223 subsonic velocities wouldn’t be nearly as effective; due to differences in energy (and therefore cavitation & destruction). We’re talking 1200 ft/lbs vs 150 ft/lbs; obviously relevant, even though the projectile is identical. The bullet shape is the same, but cavitation and destruction are VERY different.
With the .38spl vs .30C issue, you’re comparing loads with around 225 and 975 ft/lbs, respectively. Not as dramatic a difference, but still very relevant. That’s why the carbine is such a limited-range gun. Because at 200 yards or even less, it loses three-fourths of its power, and then you’re right, it probably IS no better than the .38 special is at the muzzle.
(That said, while obviously not my first choice, a .38 spl lrn at muzzle contact distance could still rearrange your world.)