A wide angle converter will reduce image quality considerably and also may add distortion and other imperfections on top of what your lens already has. If you're using an expensive lens, then putting a wide angle converter on top of that will give it image quality worse than the kit lens that comes with many cameras.
Teleconverters, on the other hand, are often designed to be used specifically with a few lenses, and feature high quality optics that only reduce image quality a bit (and are quite expensive as a result). However, there is still a drop in quality.
For example, here are some resolution numbers for a very expensive Canon 300mm f/4L IS, as tested on a Rebel XT:
Without 1.4x Teleconverter, f/5.6
Center: 1996.5 lines of resolution
Border: 1928.5 lines of resolution
With Canon 1.4x Teleconverter, f/5.6
Center: 1796.5 lines of resolution
Border 1596.5 lines of resolution