Corel Draw is a competitor to Adobe Illustrator - both are vector editing applications. Although I am more of a fan of Adobe products, when Adobe recently announced some of the new features it added to Illustrator, some Corel users were chiming in explaining that these features have existed for years in Corel Draw. So there may be some benefits there, aside from price alone. Also, I don't believe Corel is doing any goofy pricing structures like Adobe Creative Cloud.
Corel Painter would be their competitor to Adobe Photoshop. Unfortunately I've not played around with Painter enough to say how it compares to Photoshop. I tried it out again a few months ago and couldn't figure out how to do anything comparable to Layers in Photoshop, quickly got frustrated and uninstalled it, if that helps. I will say, there does seem to be a much larger base of Photoshop users, so finding plugins and tutorials is much easier.