I have been using R with OpenBLAS and MKL for a while, and it does feel a lot faster. However, I am not sure where that performance improvement comes from, I mean, what functions in R get faster when using alternative BLAS libraries?
I am guessing that the regression functions get faster, but I am not sure if the random number generator also gets faster.
A better BLAS makes vector/matrix/array operations—thus many models—faster:
The default BLAS isn't really slow, per se, though, so if you care about speed, usually writing more optimized code will get you an orders-of-magnitude bigger speedup than changing BLAS. It does depend on the task, though.