Users of both of these software packages can be staunchly biased in their approval of one over the other, but with any comparison, it is important to find out precisely what the user will be needing the application for.
CorelDraw has added a huge range of fonts recently in response to user feedback, but Adobe already had a large range so this might not put CorelDraw ahead. The new content finder from Corel gives instant access to sites such as Flickr for a range of copyright free images, which can then be manipulated using CorelDraw. In addition, tracing bitmap images as vector images has been made easier with the new software Corel has introduced.
Users of CorelDraw, especially those who were more experienced in the use of Adobe applications, all agree that vector art in the Corel programme is much simpler than in Adobe. Therefore, if you are creating images that need to be disseminated to different users or reproduced at a large magnification, you should choose CorelDraw.
On the other hand, users of Adobe Illustrator claim it is still the industry standard. If the programme you use to create your designs is the one with which most people are familiar, this can be a huge asset. Also, it is not necessary to make any file conversions when importing Adobe Illustrator into Photoshop (another industry standard), whereas with CorelDraw the file will have to be converted before importing. This can be fiddly and not always 100% successful, so if use of Photoshop is an important part of your process, then Adobe Illustrator will be the application to choose.
Finally, if price is an issue, CorelDraw is about three quarters the price of Adobe, so perhaps this is a case of ‘you pays your money, you takes your choice’.