Corel painter and Adobe illustrator are nothing alike. They aren't comparable, they do different things entirely.

Corel painter is a bitmap software. Which means you manipulate little individual squares of color.

Illustrator is a vector software. Which means that the images are recorded as a series of mathmatical equations. Things can be scaled as big and as small as you want without losing any quality like you would with bitmap software.

Painter is meant to mimick traditional mediums. It is a worthless software if you don't buy a tablet ( http://wacom.com ) to go along with it. So if you want to do illustration that looks like paintings and drawings, painter is a good choice. (example of a picture in painter: http://christmassocks.deviantart.com/art/Portrait-painting-33487791 )

Illustrator is good for things with solid or gradient colors. And smooth crips lines. (example of picture in illustrator: http://laichro.deviantart.com/art/100-000-HITS-22215849 )