Adobe does a better job with the colors without having to go through a lot of color management. The reason behind this is Corel allows you to create or open graphics without assigning them a Working Space profile. Photoshop will ask you whether you want to use the embedded profile or convert it to the working profile. Unless you understand the color management area of Corel, you are going to have to play with your colors. But working in a vector based program makes it much easier to switch out colors so they print correctly. You just need to print off a color chart and make a color palette that matches your color chart. Hope this helps.
Mark