From an end-user's standpoint I think the pertinent details are that xoshiro256** is 15% slower than xoroshiro128+ but its low bits don't fail binary rank tests, and xoshiro256** is fully (4-dimensionally) equidistributed while xoroshiro128+ is only 1-dimensionally equidistributed, and (to state the obvious) xoshiro256** has 256 bits of state and a 2^^256-1 period instead of 128 bits of state and a 2^^128-1 period.
xoshiro256**is described in the paper Scrambled Linear Pseudorandom Number Generators (Blackman & Vigna, 2018).From an end-user's standpoint I think the pertinent details are that
xoshiro256**is 15% slower thanxoroshiro128+but its low bits don't fail binary rank tests, andxoshiro256**is fully (4-dimensionally) equidistributed whilexoroshiro128+is only 1-dimensionally equidistributed, and (to state the obvious)xoshiro256**has 256 bits of state and a 2^^256-1 period instead of 128 bits of state and a 2^^128-1 period.