Ugh. Another CorelDRAW vs. Adobe Illustrator thread -with many of the same very generalized statements. I see so many of the "there's not a thing program X can do that program Y cannot" claims. And that's pure baloney when one bothers to get down to specific differences between each app.
There's lots of specific, unique features exclusive to CorelDRAW or Adobe Illustrator that make it necessary for me to use BOTH on a frequent basis. At times I really wish I could just use only one or the other 100% of the time. Unfortunately neither is good enough or overlaps the rival enough to make this fully possible.
CorelDRAW is great for allowing full sized designs. I can edit objects faster and more efficiently in CorelDRAW thanks to its tool editing set. It's a breeze to do things like align anchor points in CorelDRAW while it's more of a pain to do the same in Illustrator. You have to do extra clicking and do so carefully to avoid winding up in Flash symbol editing mode (grrr!). Illustrator has added more anchor point editing tools in recent years, but it still doesn't quite compare to the stock tool set in CorelDRAW. You end up having to spend extra for plug-ins like CAD Tools to gain much of the same object editing flexibility.
Illustrator is better at handling type & color, although Corel has made strides in recent years. Illustrator has fully supported OpenType for a decade while Corel is just now adding full OTF support at version X6 to finally take advantage of things like ligatures, alternate characters, full fraction sets, etc. Illustrator handles a number of effects more cleanly than CorelDRAW. I can paste paths from Illustrator into Photoshop layouts (CorelDRAW cannot do this since it has never supported placing AICB paths onto the clipboard). There's a number of handy, free plug-ins for Illustrator that I can't use in CorelDRAW -like the path area plug in from Telegraphics.
Both CorelDRAW and Adobe Illustrator are very good programs to use for creating vector-based graphics. Both are "professional" level applications. However, both have their own specific strengths and weaknesses.
One thing is for certain: MS Publisher isn't remotely as good as either CorelDRAW or Illustrator. It's not even as good as Inkscape -and that's an Open Source vector drawing app.