When you export or print shadows they are converted to bitmaps. This is the way all vector graphics program simulate soft shadows and that includes Illustrator. (The same applies to transparency, feathering and other effects).
Our tests with Xara X EPS show that shadows should work perfectly well (as bitmaps though, but if you set the transparency resolution to be decent this shouldn't be noticeable). Illustrator works the same way, except its shadows are not dynamic as they are in Xara X - zoom in in Illustrator and you can see the pixels. In Xara X are shadows act much more like true vector objects so they are resolution / zoom independent, so you will get higher quality results. But in the end when printed or exported all programs convert to bitmaps.
If shadows are not appearing correctly in Xara X EPS then I'd like to see some files showing the problem so we can investigate.
Gary is correct that only more recent Illustrator versions support transparency and effects such as shadows. We plan that a future version of Xara X will have improved Illustrator and Photoshop import / export, but it's not easy since this is a never ending game of catch-up.
If you want true vector shadows then the only way is to draw it as simple shapes, perhaps using blend. It will never be as realistic as a true feathered shadow though.
PNG is a viable alternative. I know some users export the shadow as a PNG bitmap and import that into whatever app they are using. Even though this is not a vector, in the end it's the same thing as you'd get from using native Illustrator soft shadows since, as I say, they are simulated using bitmaps in the end anyway.
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