There is unfortunately no good answer to this question, as it would completely depend upon the algorithm, MPI implementation, communication network, vendor-tuned BLAS library, etc., etc. However, I can safely say that Elemental is always competitive with ScaLAPACK in performance. The Elemental papers on my website (pick between the preprint or journal article), http://www.stanford.edu/~poulson, go into this in more detail, but keep in mind that the article was written a couple of years ago, when it was still a fledgling library, and so the tone is a bit more aggressive than necessary.

With that said, the main advantage of the library is its high-level of software-engineering, which tends to encourage the rapid development of new features. It is actively used within a large number of research projects.