How does a 38 Special +P from a 4" bbl. stack up against the 9mm?
It depends entirely on WHICH ammo you are comparing.
Suppose I compare a modern .38Spl +p with an expanding bullet that actually expands against the original 9mm load which was a 124gr FMJ at 1050fps from a 4" barrel.
Not quite the same thing is it?
if you know where to look, (or you're old enough to remember) there are decades and decades of gun writers ALL rating the .38 Special above the 9mm for self defense. The "why" was simple. In those days, there were NO factory loaded JHP bullets. The .38 Special was loaded with lead bullets which would, sometimes, deform and expand a bit. The 9mm was loaded with FMJ bullets which would not.
Today, there is a much, much wider selection of loads in both calibers, so comparisons have to be as much "apples to apples" as we can make them, or they're essentially meaningless.
And, don't take anybody's velocity numbers as gospel for what you will get from your gun. Probably close, but variations of as much as 100fps are not unknown.