The book index can do some things that full text search can't do, it's true. But full-text search can also do a great many things the "back of the book" style index can't do, especially when quality of back-of-the-book indexes varies highly (generally correlated to how much you could spend on paying skilled expert(s) to create them, and always has; it's just that publishers used to invest more in them, at least sometimes).

If you could only have full-text-search or back-of-the-book index, which would you pick?

It doesn't matter, cause you don't have a choice. I disagree with article that it "doesn't need saving", if the author meant that it's future is secure. The back-of-the-book index is dying, those that remain are seldom of much quality. The expertise and skill and methodologies of creating manual indexes will soon be lost. I am glad some are trying to document the back-of-the-book index as a technology, before it's gone.