I have the new LCP custom. I had 2 of the others versions before this one. The trigger system is what made me change. The pull is better and the shape of the trigger eliminated the pinched finger between the trigger and guard. The sights are better, if you use them.
For me, this is a "weak hand" pocket pistol for serious, upclose work. For that I don't need sights, but I do want a very good trigger.
I have the newer version of the LCP. I just got it a few weeks ago. I decided to get the standard version and not the LCP Custom. When I compared the two pistols side by side I found the trigger pull to be exactly the same. The custom has taller sights and the red trigger. I felt like the taller sights would snag with pocket carry and the red trigger had sharp edges that I didn't like. The custom also has a stainless steel guide rod. I replaced my guide rod with a stainless steel rod for about $8. The trigger is more comfortable for me and the standard model has improved sights over the original LCP. It's not a target gun and the sights are good enough. Mine also came with a laser for low light situations. This is a point and shoot gun for close up self defense maybe out to 20 feet or so. I also added a Hogue handall grip and a 13# recoil spring to help with the recoil. So far I love the gun. I shot 150 rounds the first time out with no problems what so ever. I don't think you can go wrong with either the custom or the standard version. The trigger on the LCP has always been the primary issue and Ruger has fixed that with the newer LCP's. Good Luck !!!
I have always been a Ruger guy, they are my true Love of firearms. But that being said I always carried the S&W BG380 with laser. I really liked that gun and the Ruger LCP with the no sights really did not make me fancy it at all.
Then the LCP Custom came out and I ordered one on the spot. I like the trigger being long and a little stiff great for pocket carry without a holster if wanted (I do both) and the sights just made it feel like a real gun. I have no problems with the sights snagging that I have noticed.
One thing about the BG380 was it could be unreliable (Mine was reliable) from what I have read. So I traded the Bg380 in for the LCP custom and never looked back.
Perfect pocket pistol now.