As Brushman mentioned, you can't compare the two. They're totally different types of apps. Photoshop is a bitmap editor. The two comparable apps in the Corel line would be Photopaint or PaintShopPro. Draw is a vector editor and would be comparable to Illustrator or Freehand.
You would *never* use a bitmap editor to design a logo. You would always want to use a vector editor to design a logo because the vector files will be totally scalable in size, will not lose quality when scaling size, and can be exported to many different formats and color spaces for alternate uses. A well-designed logo should work in one/two colors as well as four color spaces.
If you're not familiar with the differences between vector and raster (bitmap) applications and you're wanting to design logos, I'm sorry to be blunt, but you may want to go back and take some refresher courses in the applications. Otherwise, your best bet is to download the demos of the applications. That is the only way you're really going to be able to tell what will be best for you.