My personal take is both do the same thing - in different ways.  I personally prefer Corel Draw - as Adobe tries to have you use the keyboard with one hand, and the mouse with the other.  Zooming is a primary example.  It is easy to zoom in and out with just the mouse in draw - not so much with Adobe.  The other side of the coin, Draw seems to be a 100% Vector based platform, while slowly adopting raster capabilities (drop shadows and transparencies) while Adobe seems to be primarily a Raster based editor that incorporates vector capabilities.  This can be good or bad - depending on what your project requires.  I think you will find more native support with hardware options (engravers, routers, vinyl cutters, tables etc) with Corel then you will with Adobe.  However, my info on this is a bit dated, and things may have changed.

Bottom line, I find Corel easier for first time users.  Adobe tends to have a strong tradition of "initiating" users before the basics are unlocked.  However, Adobe has more third party support (especially for Photo Shop).

Thanks for opinion. Which program requires more system resources?

I guess it depends on which versions you are lokoing at.  Off thetop of my head, I want to say Adobe, but I could be wrong.  Corel seems to stay relatively lax on the the resource hogging, but I have some issues where some system configurations just do not get along with Corel, while identically configured systems seem to have no problems.  So I am not sure - definatively - which one will be the better option for resource management.  PArt of the answer is going to depend on your inteneded application.  For high end, large format output's you are going to need WAAAAAY more resources then you would need just to launch the program.  If your preprinting work will involve catalog or multipage flyer layout - with high resolution graphics, I think you will have more then enough resources available at your disposal then either prgogram will require.  If in doubt, leave your system scalable (more memory, more HDD space, etc).

What application is preferable for use for web graphic mainly? (creating logos, banners, not for preprinting)

Sorry it took so long to get back - been swamped.

For web use, Adobe Photo Shop.  It would be considered industry standard.  My personal preference is Corel Photo Paint for all manipulation and special effects - with a few exceptions for some of Adobe's camera tools.  However, hands down, I think Adobe has much better color correction than Corel.  If you can get by with using both, you will find your particualr style will excel in some areas with one platform over the other.  If I had to only choose one, it would be a tough call.  I prefer Corel, so that would be my personal preference - and it is mostly for silly reasons.  I like the interface better, Adobe also believes proper usage should ahve one hand on the keyboard, one on the mouse.  Everyone knows this is silly, you need the free hand to hold the Red Bull - or to lean on....

The only real draw back that I personally don't like about Adobe, is all the plug-ins.  It seems everything REQUIRES a plug-in instead of being able to create free-form.  At least this is my take.

Thanks for opinion.

Its intersting to know which from previous Adobe Illustrator versions has better performance(less crashes)and use less resources?

Unfortunately, I am not that versed in Illustrator.  I know enough about the program to know I would always use Corel for any vector layout work.  Photo Shop, I have slightly more experience, using it since about version 5.5, but not enough to know the difference between a bug and a system "quirk" or platform difference.  Check the Adobe forums here on Tek-Tips.