Wow, I'm honestly floored by the number of people who choose ADJ over Chauvet. I think its very important to compare similar product lines from each manufacturer.
Chauvet has two lines of offerings- their "DJ" oriented fixtures, and their "pro" line.
All products I own from Chauvet are their pro line, however- I would trust their DJ line over American DJ any day. In my opinion, they seem to be more rugged and reliable than anything I've ever used from ADJ. In my experience, they break down far less often than their ADJ counterparts. Chauvet has caught a bad rep for quality control and customer service in the past, but they have really taken steps to improve this and are putting out some very quality products. (Their LED Q Spot line of movers being a prime example)
Now, Elation does have some nice offerings, but its more fitting to compare them to Chauvet's Pro line. Even still- I'd choose Chauvet over Elation any day.
Finally, American DJ is NOT known for their customer service either... I have heard horror stories of people trying to get fixtures serviced, DOA's, replacement parts etc. It's difficult to maintain a service department with such a huge product line to maintain.