Project64 v1.6 isn't outdated, it's the most recent, not counting the 1.7 beta.
Project64K v0.13 is the latest version of said emulator. The only reason you'd want to use it is to play online (and PJ64K fails spectacularly at that every now and then). Since the K version is based on Project64 1.4, you definitely don't want to use it outside of online play.
P.S. The Project64 team didn't make Project64K, thus taking no responsibility for it, so technically this thread is in the wrong forum.