I'm a fan of replicating the book as accurately as possible, in PDF form. So I would try to scan the illustration as "complete" as possible - because let me tell you, it's a little tricky using a flatbed scanner to get a good shot between the pages.
Also, it depends very much on the illustration. If it's something simple with most of the details in the middle of the page and a simple colour or colour gradient at the edges, I could just fill it in and none will be the wiser. But if it's a photo or something, I would probably have to crop it so it doesn't look blurred at one edge. But I don't know... I haven't really come across any book with edge-to-edge photos before.
If it's an ePub or Mobi we're talking about here, you could probably get away with hacking both parts together - again, depending very much on the illustration. For instance, most people look at the middle of an image first. So they'll easily spot a big tear right in the middle (or a blur, whatever). Both images would have to line up pretty well.
Alternatively, place one half on one page, crop out the bad part, and when they switch to the next page their minds will automatically fill in the gap. Experiment with this a little.
Because it really doesn't matter if 80 px are missing on each side. Crop each half to 600x800 and they won't care. Heck, they probably won't even notice, unless they have the paperback with them and thoroughly check it for details. But I bet the written stuff is much much more important than one illustration. It is a book, after all.