http://en.wikipedia.org/wiki/Electron_crystallography gives a pretty good comparison of the two. Basically electrons are much more strongly interacting than X-rays, so they are restricted to very small samples. In a previous life I used electron diffraction on mixtures of sub-micron crystals to identify what was present in the mixture. This would have been very difficult to do with X-rays.
However in the electron diffraction (at least the measurements I did) one measurement gives you only one plane so using it to do a full structure would be painfully slow. With X-rays diffraction you get scattering from all the planes in one measurement.
Admittedly my experience is many years out of date, but my recollection was that the techniques are complementary. You'd use X-rays for your routine structure determinations and electron diffraction for special cases.