More recent version of iTunes, rather than storing the artwork in the ID3 tag (or whatever the equivalent for AAC files is) of the file, store it in a folder called 'Album Artwork' in the iTunes folder and put a reference to the location of the artwork in the iTunes library file.
That means even if you copy the folder across when you move your library, if the path to the Album Artwork folder has changed, the reference in the library file will be wrong, so the artwork won't show up. You used to be able to edit the iTunes library file but I don't think you can any more. So the bad news is you can't just update the iTunes library file with the new path. The even worse news is the artwork isn't even stored in easily readable form - I think the .itc files in the folder are actually just renamed JPEGs but that still doesn't help you matching image to track.
There's more detail on
this page, which also includes links to a couple of useful applescripts that may help you out, particularly the first one on
this page. You could also use the 'get album artwork' option in iTunes to download some of the stuff that's missing again or use something like coverscout to do it for you. However I should warn you Equinux (the makers of coverscout) use some of
the most braindead and half-baked licensing DRM I've ever seen on any platform. Ever.
And yes, it was absolutely bloody stupid decision on Apple's part to store artwork this way rather than in the song file itself. I really don't know why they decided to do that.
Jon