That's a flame starting question, but I would suggest Illustrator if you have the desire to put in the effort to learn the program. Printers will have less problems with Illustrator files... with the format, with color seperations or preflight, gradients, etc. Also, depending on the line of work you are in, knowledge of Illustrator may carry more weight than Corel.
Most of the complaints from the Corel camp of users is that Illustrator is harder to use in certain instances, or harder to learn. Feature for feature though... both programs are roughly in parity.
I have avoided corel, or working with people that work with corel since my days working in the print design business. The more complex their files were, the longer we would have to spend rebuilding them to prepare them for printing. I'm sure corel has gotten better over the years, but Illustrator is a proven workhorse with good tools, good help, a wide & knowledgeable support base, and a long history of being great at what it does.