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.
Indeed, we didn't chose Elemental over ScaLAPACK; we used Elemental to replace LAPACK because it was impossible to refactor our code to use ScaLAPACK without absolutely ruining it forever. The ScaLAPACK interface is horrible and should only be used inside of a higher-level library interface that hides its ugly, ugly control structures.
From my perspective, Elemental is primarily about human performance. That it scales to thousands of nodes of Blue Gene and achieves performance on par with (and in some cases significantly better than) ScaLAPACK is really icing on the cake. Granted, I really like scalability and performance, but I will not ruin my code in the name of these things.
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.