ChaCha20/20 is a more conservative choice (i.e. there are classes of attacks on ChaCha20/8 that would be infeasible against ChaCha20/20) but runs somewhere between 1/3 and 1/2 the speed of 20/8.
The performance graphs show a whole bunch of PCG generators.
You absolutely can predict the Mersenne Twister after 624 outputs (there are several blog posts out there). The Mersenne Twister is also huge (2K of state) and some people claim that as a result it's not cache friendly.
But yes, it's a new thing, so it needs people to look at it.
But a tiny change (XorShift*) is enough to get a generator that passes empirical statistical tests.
The page about other RNGs has lots of good info about this stuff.
