Up to a point they are just tools.
What exactly are you going to be using it for, signs only?
Where do you plan on going with your business?
Will your vendors have a problem with any program you get?
PC or Mac?
Are you going to be getting Photoshop?
Is money an issue?
Do you have any experience with either?
If money is an issue and you are on a PC, Corel is a no brainer. It has way more bang for the buck.
Once you get into more than just signs, the line gets a little blurry. I have quite a few print only designers who get the job done with their Corel but they still use In Design and Photoshop for page layout and photo manipulation. Now that Adobe has bought Macromedia, who knows what will happen to Illustrator, there has been talk of Illustrator having more Freehand tools, but they may keep Freehand for a while too.
Don't be fooled that Corel is prefered for sign design, or Illustrator is for graphic design, they are both great tools for both. It's just where you are going to take your business.
I have both, prefer Illustrator over Corel. It's not because Illustrator is better, it's easier for me to use, it serves my purpose because it playes nicer with my Flexi, Photoshop, InDesign, Acrobat, Quark, AutoCAD, GoLive, my vendors and with CadTools I can do my drafting in Illutrator and keep a usable file for sign companies to make the sign.