.380 is adequate for the majority of self-defense situations and .380 pistols generally hold more ammunition than the small-framed revolvers.
I don't carry (or own) a LCP, which I find unpleasant to shoot. but I do carry a couple of larger .380s: a Beretta 84FS Cheetah and a Walther PK380.
The Walther is an extremely pleasant gun to shoot, is accurate and not difficult to conceal in normal street clothing. I have a total of nine rounds available and I have seen the PK380 advertised for as little as $299.00 at Bud's Gun Shop.
The Beretta is also pleasant to shoot and holds 13 rounds. I will be the first to confess my attachment to the Beretta is largely because it is beautiful and fits my hand like few other handguns. It's relatively heavy, making belt carry mandatory, and the double-stack magazine means a thick grip. Circumstances that will allow the comfortable carry of the Beretta will also allow me to carry either my Beretta PX4 Storm or FN Herstal FNP-9.
I don't like the postage-stamp pistols for two reasons: First, they don't lend themselves to frequent practice with carry ammo. Second, they are not as controllable for follow-up shots. Say what you want about it; physics is physics. You may not feel the pain, but the gun is going to jump and buck just as much in a SHTF situation as it does on the range. Part of the problem is the size and weight of the gun itself; the other part is the tiny grips. The pinkie finger plays a surprisingly large role in grip strength, which in turn plays a large role in controllability. These are among the reasons it bothers me when a newbie picks up one of these tiny pistols as their first handgun.
IMHO, comfortable concealed carry is an important consideration but if you are going to go armed at all, competence with the weapon is far more important. There are plenty of owners who, for one reason or another, will make the effort to become competent with their LCP or Seecamp, but I would bet money there are even more owners who won't but might have if they had purchased a more suitable firearm.