It depends strongly on the subject. For the majority of science and engineering subjects, books win hands down. Some recent examples:

1. Chemistry. Want to know the details of a common battery chemistry? The regular google results aren't helpful -- they're a combination of grade-school demos and premeds incorrectly explaining electrochem MCAT problems to each other. The google scholar results aren't helpful because the relevant literature is too old to be indexed, the trail of scientific discovery is too difficult to quickly and correctly follow, and/or it's in german (with shit OCR so google translate doesn't work).

Meanwhile typing "battery chemistry" into the library search system brings up several relevant tomes, the first one of which has exactly the discussion I'm looking for condensed into the space of several pages. A quick google search reveals that this page was never posted to the searchable internet.

2. Math (or Chemistry or Physics). Want to know the precise definition of a symbol you keep seeing? Too bad: google doesn't know how to search for formulas or symbols (btw, I'd love to be wrong here). Naturally, the journal article you're reading doesn't bother to define it, so you're SOL.

Unless you find a similar discussion in a book -- in that case, you just look in the front or the back and 80% of the time you'll find exactly the precise definition you need. The other 20% of the time you have to binary search backwards until you find the point in the book at which the symbol was defined. Easy enough.

3. Engineering. Want to find a cohesive discussion of X? If you go to google, you'll find 30 ppt presentations with piss-poor production value, big useless unexplained formulas with undefined terms and not enough discussion to fill in the blanks. In contrast, if you check out a book you can find a cohesive introduction via the index. If you're lucky, it even includes motivation: "we argue that X is a linear transform, we project it onto basis Y, blah bla blah" rather than a big nasty tensor equation. Maybe you read the first few paragraphs in the chapter if it's too hard and you need pointers to further supplementary info.

4. Computer Engineering. If nobody is willing to pay to make good digital documentation, sometimes engineers are still able to get funding for a book. I learned about Mach and mDNS this way -- the books were amazing compared to the digital docs and well worth 5x their price (by which I mean their printed price, not the $0 I paid to check them out).

5. Open Source. Books are a great open source business model because two magical things happen that wouldn't happen otherwise: 1. the author of the documentation gets paid, 2. the culture of bookwriting imposes minimum quality standards on their documentation. You get to learn the story. You feel like you're along for the ride, not someone who got dropped into a room full of people who already know what's going on and cantankerously respond to your questions with "google it" despite the fact that your post documented the search terms which failed to produce useful results.

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Books have a degree of cohesion and completeness that websites and journal articles lack. Since it sucks to follow printed citations, authors err on the side of including everything you need. The culture of bookwriting figured out long ago that you need to include the boring stuff too -- and that's a lesson the internet has yet to learn (if it ever will).

Also, the internet hasn't been around for long enough to capture every subject's burst of initial excitement + willingness to write about it. The list of things the blog-o-sphere doesn't know or care about (literally) fills libraries.

Science & Engineering bloggers willing to write highly informative articles are a scarce bunch. Historically, that communication happened in books, so that's where you often need to go to get what you want. The situation a lot better in computer engineering; y'all don't know how spoiled you are :P