I've owned several Airweight snubbies (now have a Ruger LCR .38 in that role) and have a couple of LCPs.
The LCPs are easier to carry without notice. They're tiny and light. And they hold 7 rounds and reload in a twinkle. I don't think you can make them hit as hard as you can a grown-up .38 Spl (even out of a snub), but they will penetrate all you need with ball ammo. I also find them easier to shoot quickly and accurately than a J-frame - at least a J-frame wearing concealment grips.
The Airweight, you can customize. What kind of stocks do you want? Concealable or controllable? There are some that do a fair job of both, but I find that with my (medium sized adult male) hands, the LOP on an open-backstrap J-frame (the most concealable sort of grip to use) is too short for me to be especially accurate. (If I use bigger grips, they can be great - but they're harder to conceal, and the entire point of an Airweight J is maximum concealment.)
The revolvers are simpler - you can hand it to your less-skilled wife and she can use it fine. The LCPs - well, not everyone likes a semiauto.
Tastes great/less filling - your call. I see a role for both guns . . . but find I carry the LCP more in my present-day life.
Of course, sitting around here at home, I have an Improved I-frame pre-Model 30 6-shot .32 S&W Long with hot (1070 fps/100-gr RNFP) handloads in a Bell Charter Oak IWB holster. So . . . I might not be a representative sampling of popular thought.
