It is a constant trade off size versus convenience.
If you knew you were headed into a fight you would take the biggest handgun you had...and a shotgun...and a rifle. Then again if you knew you were headed into a fight it might be advisable to change directions.
If you are in your "man about town" mode, you want to have something to help be prepared in case you can't avoid a violent confrontation. First question is, "Do I want to be shot with a .380?" The answer is no, because I don't want to be shot with anything. So if an ultra compact like the LCP is something that you will carry regularly, then I think it is a fine choice. In the trade off the LCP offers a very small, very flat package for a slightly anemic round like the .380ACP (also know as 9mm short), but never the less it will help you settle the argument.
Would a Smith snubby is .38 Special be better? That depends on whether you'll regularly carry it. Even for a small gun the J-frame Smith's are quite a bit larger than something like the LCP. But you get some more "oomph" if you have the pull the trigger. There's your trade off.
JD will be around in a bit, and he (like many others) is not comfortable with a 90 grain .380ACP. He trades the convenience of carrying a small, lightweight pistol for the, I don't know, lets call it "assurance" that comes with a brickbat 1911 spitting 230 grain .45 ACP fireballs. I can't say that I don't see where he is coming from, cuz I like big guns & big bullets too. However, in the summer I've been known to pocket carry a Smith 442 or (don't laugh guys) a Kel-Tec P32 (before the 3AT or the LCP models came out).
The tradeoff in carrying a gun like a .32 Kel-Tec is small bullet/mediocre reliability for super-ease of carry. I considered my risk potential and accepted that a P32 was all the gun I was going to carry that day. Those decisions are personal for everyone, but I say better the .32ACP in your pocket instead of the .45 ACP that got left on the nightstand.
Risk assessment is part of it as well. Would I suggest a night manager at the local stop & rob doing his bank deposits carry a micro-compact .380? Probably not, just like I wouldn't go into the street as a police officer carrying anything less than a full-size fighting pistol.
The long and short of it is that you have to decide what your risk potential is, and decide what the biggest gun you think you will regularly carry is.
One more thing, and I can't remember where I heard this, but I liked it so I'll pass it along: "Carry guns are supposed to be comforting, not comfortable."