Adobe Illustrator has long been, and is still the industry standard for creating vector graphics. Still, Corel continues to make inroads into the freelance, home business design markets, partly because of the increased functionality in Corel upgrades, and, because Corel is SO much cheaper.
I started off with CorelDRAW 3, but quickly picked up on Illustrator, at first, because it WAS the industry standard, and a working knowledge of most Adobe products was pretty much required of anyone converting design skills from paper to digital media. (Illustrator, Photoshop, Pagemaker and others)
I never really looked back, and never upgraded my Corel suite beyond Corel 4. The Adobe products worked together flawlessly, and the CS versions, even better.
I am NOT putting down the Corel products. They have managed to remain successful, and service bureaus like printers and copy centers commonly accept the Corel formats as readilly as the Adobe files.