I found the .380 911 to be very slightly wider and heavier than the LCP II. The 911 will print more in a back pocket, and the beavertail may stick out over the top of the pocket (depending on you wardrobe). For front pocket carry, the 911 wins hands-down due to the external safety. For back pocket carry, I go with the LCP II.
The pocket holster that comes with the LCP II works much better than the one that comes with the 911, but replacements can be picked up fairly cheaply. The biggest issue I had with either pistol involved break-in. The 911 took about 200-250 rounds of ball ammo to start working 100% reliably, but it has been reliable with both FMJ and JHP ammo. The LCP II fired ball ammo 100% out of the box, but didn't reliably cycle most self defense ammo until I had put 100-150 rounds of JHP through it. A few months ago, it would've been much cheaper to break-in a 911 using the ball ammo. Now that all .380 ammo is impossible to find, and JHP is selling for prices that are close to FMJ, it is essentially a tie.
The sights are much better on the 911, and even the fiber optic sights on 911 Alpha are much better than the blacked out LCP II sights. However, a little orange paint on the LCP II's front sight helped a great deal. If you plan to carry ball ammo, and carry IWB or in a suit or rear pants pocket, go with the LCP II. If front pocket-carry is in your plans, I'd go with the 911.