PL3 is aiming to be a universal payload that everyone will use in the future. It was made to combat all the other payload releases (PSGroove, PSFreedom, Hermes etc), and make it so everything was in one place. Initially people had a lot of problems with PL3, but most issues are now fixed.
As of now PL3 doesn't have as large an index of homebrew applications, mainly due to the fact that it is newer than hermes, and due to it using a different syscall it won't run Hermes based applications without modification. However, PL3 is slowly becoming the preferred payload by many, and some people also regard it as more stable.
It's not directly related, but here is a post by KaKaRoTo (The PL3 creator), stating why he favours the PL3 payload over competitors: http://www.ps3news.com/forums/ps3-ha...ss-114109.html