Let's make a realistic and fair comparison of the 22 Mag and the 38 Special when fired from a defensive handgun, specifically a snub nose revolver.
According to Hornady
their fancy "Critical Defense" load achieves the following:
Test Barrel (1 7/8 V") Velocity (fps) / Energy (ft-lbs)
Muzzle 1000 fps /100 ft-lbs
A 38 Special firing 125 grain +P ammo will get about 850 fps for 200 ft-lbs of energy.
The frontal area of a .223 bullet is .35 in^2.
The frontal area of a .357 bullet is .56 in^2, a 60% increase.
A 45 grain .224 bullet has a sectional density of .114
A 125 grain .357 bullet has a sectional density of .139, a substantial improvement.
A 125 grain bullet weighs almost three times (2.777) as much as a 45 grain bullet.
So a 38 special fires a bullet that weighs almost three times as much, has TWICE the energy and 60% more frontal area and better sectional density.
The fancy new 22 Magnum loads are better for SD than 22 MAG rifle loads, but mostly because they reduce flash and blast. They are not magical bullets that transform the 22 Mag into a good SD load. When you cut out the tumbling bullet nonsense, the unequal barrel length comparisons and the wishful thinking, they're just not up to the task.
It's a good thing that they allow more shots, because if you ever actually have to use one for real you're going to need them.