Dan:
By education and profession -- at least in my early years -- I'm an engineer, so I try to respond to threads like this on TFL with physics-based information. A comparison of the two options you pose follows:
a) The .38 Special (presuming 1050 fps) provides 12442.5 ft/lbs of muzzle energy
b) The .357 magnum provides 17500 foot/pounds of muzzle energy
Since both rounds have essentially the same diameter -- about 9mm or .36 inch -- the "wound dynamics" related strictly to the diameter of the round will be basically equal. Therefore, presuming the same type/construction of rounds (i.e., FMJ versus FMJ, HydraShok versus HydraShok, etc.), the .357 magnum loads should be considerable more effective, about 41 percent if you believe "pure physics".
Of course, the problem is handgun/ammunition efficacy is a LOT more than "text book" physics. For example:
a) Shot placement is absolutely indispensable; will you fire one round more accurately than the other?
b) Your particular "mission" and "environment" are also key. Penetration of automobile glass and bodies, for example, demands a high velocity round and may fundamentally exclude the .38 Special. Similarly, home defense in an apartment building may make the .357 magnum less desirable, due to potential shot carry-through into adjoining homes.
This is a long way to articulate a simple message: All other conditions being equal, the .357 magnum is clearly the superior defensive round. However, your personal tendencies (like better accuracy with one of the two loads) and your likely "mission environment" (such as LEO versus civilian or apartment complex versus isolated rural home) are also very significant elements in your choice of defensive rounds -- and firearms, too, for that matter.
Hope this helps and happy holidays.
[This message has been edited by RWK (edited December 22, 1999).]