On e-book readers like Kindle, a profound disagreement. I can easily find what I'm looking for in a 1000 page book even without using an index in less time than it takes to type in a search query into Kindle's searchbox (especially since I switched from the old keyboard Kindle to touch-only Paperwhite). If there's a well-curated index at the end of the book, it's only that much better.
I think software could get somewhat closer to paper experience, but it needs to be faster. As long as random page access takes more than ~100 ms from selecting the page to full render (and in my experience, it's often close to 300-500 ms), you cannot really flip through an e-book the way you would through a paper book.
(Tangent: it's another of many cases where performance actually matters, because the difference between lighting fast and fast enough to tick boxes on your sprint plan is entire family of use cases.)
"I can grep through the entire set of books for something in particular"
What software do you use for this? I'm guessing you're not literally running grep at a command line on your mobile.
So what software do you use that allows you to search through multiple ebooks? Is there an Android or ios equivalent to DocFetcher?
printed books on the other hand give away what you are reading -- unless you put them in those fancy covers. and that is if you can even find the right size.
you don't get the eyes and no one will ask you what you are reading on your phone. never thought about it that way before...
For recreational reading, I strongly prefer real, printed ones.
For reference materials, I strongly prefer electronic ones (stripped of DRM and converted into a non-proprietary format). I can keep my entire technical library on my phone and I can grep through the entire set of books for something in particular that I need to find. I remember the days when my technical library was in printed form. It took a lot of space and often I'd be unable to predict which book I'd need at home vs at work, and end up not having it available. On this front, electronic books were a total game-changer for me.