Well, in any event, even if you end up cutting out the messed up part only or the messed up part with some of the perfection of that second copy you'd end up damaging the book regardless of the fact. So that you know what happened in my case, here's an example. There's a great book called the Sesame Street Word Book with various segments throughout the book with all the characters drawn in a way that they almost look life-like, at least the human characters do, with the relevant words highlighted. One page tells you about professional jobs and shows Gordon as a science teacher, Bob as a music teacher, Susan as a nurse, and Oscar the Grouch as a taxi driver. Well, the book has a segment where the Count von Count counts up to 20 using various items from his Transylvanian castle or haunted home. The numbers were all differently colored and had a nice style to them, so I tried cutting them out leaving one page with the items for 1-8 still bound to the book, but removing the entire page with the items from 9-20 from the book, and consequently lost that page and the first page of the Shapes pageant that follows. Again, my best recommendations would be to take the one book that's completely perfect and copy what's missing from the second book and then paste it onto the second book. Sure, this would also deface the original second book, but at least it would be only a superficial fix to get the missing picture, and you won't regret mutilating either book.
Hope this helps and have a good day.