Where exactly is the better ballistic result? Tests show that the "smaller" .38spl penetrates deeper with a similar sized expanded bullet. If the energy advantage of the .44 was applicable, shouldn't it then push the similar sized expanded slug deeper?
If not then, the implication is that the surplus energy has been transferred into the target. I understand the rationale: Its like pressing your open hand slowly down through the surface of a body of water - there is little resistance or disturbance and you can press as deep as you can reach; as opposed to slapping through the surface as fast and hard as possible. Big impact, big splash - much more "energy transfer", if you will.
The problem with that analogy for the purpose of this comparison is that when slapping your hand through the water, you'll feel the difference too. It will hurt a lot more, meaning that the harder impact affects the projectile (hand) as well. This is what results in the deformation or expansion of the bullet. If the bullet resists expansion or deformation due to it's hardness (or a more slippery shape), that energy still has to go somewhere should result therefore in deeper penetration. The .44 expanded very slightly more (proportionately way less, actually) and penetrated a lot less than the .38. Why??
By your argument, the .44 "hits harder" - transferring more of that energy into the target. But we know that even a .44 magnum cannot impart enough energy into a human target to throw it backwards. That's simply because of the difference in mass between bullet and target - even when you factor in the kinetic energy of the relatively tiny projectile. Another factor that limits the real world effect of the largely mythical "energy dump" into the target is the relative softness of the human body and the small frontal area of the bullet. Like poking a pin into a marshmallow, no matter how hard you do it, the hole will still be the same size and the amount of damage will hardly change.
Modern expanding bullets create a parachute effect that results in a bigger hole and more energy absorbed by the target *AND THE BULLET* but at handgun velocities, the effect is simply not significant enough to be deservedly referred to as "stopping power".
As far as the 11% (?) greater surface area of the .44 goes, my calculations show that the hole made by the .38 FBI round - .636" X 15.6" deep is actually a bigger hole than the .671" X 13.75" deep .44spl hole. (4.95 cu.in. vs. 4.86 cu.in. - talk about splitting hairs!
) That is assuming all 15.6" of the .38's hole remains inside the target. If it doesn't, as was pointed out, there's going to be an exit hole.
The point of all this? It just leads me to maintain that within a reasonable range of mainstream handgun calibers, the differences in bullet size and kinetic energy relative to terminal ballistic performance in a personal defense scenario are miniscule, subjective and more pertinent to bragging rights and arguments than real world effectiveness.
More powerful rounds can penetrate hard barriers more effectively but that capability does not make them significantly more effective at "stopping" a living, hostile, 180lb-plus aggressor. Once you have 12" or more of penetration and anything thicker than an ice pick, adding more in factors of a few hundredths of an inch will make little difference.
Carry what floats your boat, learn to use it well and never assume that the caliber of your handgun by some potent "over .40" magic will make you any safer or more lethal than the guy with a .38 Special (let alone a .38 Super).