Which is better: CorelDraw, Photoshop or Illustrator?
I would rather say that it is not a big deal if whatever application you are going to use, it’s your skills and creativity that matter most. If I am an expert on using CorelDRAW, of course I would say that CorelDRAW is better among others. The same is true if I am an expert user of Photoshop or Illustrator.
CorelDraw, Photoshop and Illustrator Differences
It depends on what is the purpose of your project and how long you had been using a particular application. However here are some distinctions among these applications:
Adobe Photoshop is actually an image editing software like Corel Photo-Paint nonetheless, the newest version of Adobe Photoshop have advance features for making 3D graphic arts and movies and it even support vector data. Rasterized objects can be converted to vector by applying the “convert to smart object” command. Hence, this application is now suitable for any graphic design projects. In fact, it has now DESIGN workspace.
Adobe Illustrator is very effective when you’re making illustrations (as what its name means) specially its mesh tool, you can have a great tints, tones and shades in your illustration by using it. When you drag and drop images to Illustrator, the object is automatically converted to vector file which will allow you to resize the image at many times without damaging its quality. Adobe Illustrator has more special effects compared with CorelDRAW.
CorelDraw on the other hand have features that are more appropriate for desktop publishing. Unlike Adobe Photoshop and Illustrator which you can only make one page in a single file, CorelDraw enable you to create multiple pages in a single file. It also has a barcode maker plug-in which allows you to insert barcodes on your design especially when you are making product packaging or gift vouchers. CorelDraw is like a combined InDesign and Illustrator. (InDesign is also a product of Adobe that is very suitable for desktop publishing.)
My Personal Choice
The problems when you do your layout with CorelDRAW and edit your image with Adobe Photoshop are the shortcut keys because they have a lot of differences plus some trouble on exporting and importing files from one application to another. That is why, personally, I prefer to work with Adobe Illustrator because I do use Adobe Photoshop for image editing and their shortcut keys are almost similar plus the compatibility of the software. Thus, it speeds up my work.
All of them are great when you are going to use them according to their purpose.
Remember that we, the graphic designers and artists, are being appreciated because of our design and artworks and not because of the application we use.
I know that you also have something to say; you can add it as comment.
Thank you for reading. Godspeed!

Well, i am a corel draw user, and i have used for so quite a number of years now, i enjoy using it, i started using Corel 4, i have gone through all other versions. i like Adobe Illustrator as well because of its colour pallet and these other tools that corel dont have up to now. hence my draw back in illustrator is when i want to crop something. Hence i enjoy using them both.
As you have said its not the application that matters but the project and how best one is on the application