AHD seems to think they're mostly synonymous but illuminate might could be a little more broad ranging in meaning. They both derive from the same Latin verb, illuminare and would seem to be prime candidates for prescrip venom, but you hardly ever hear illumine so maybe that's why you never hear anybody complaining about illuminate.

http://www.bartleby.com/61/82/I0038200.html

http://www.bartleby.com/61/87/I0038700.html