From my perspective, the biggest library in the world is the one nearest to you and the best library is the one that has what you are looking for. Lists of the biggest libraries in the world do not take into account the huge collections of books and other items being accumulated by the online websites such as Google Books or other such websites. But, here are some links to websites that have listed the largest libraries in the world and in the United States.
- List of largest libraries - Wikipedia
- List of the largest libraries in the United States - Wikipedia
- The Nation's Largest Public Libraries: Top 25 Rankings | Professional ...
- 10 Biggest Libraries In The World - O, Pish Posh!
- 5 Largest Libraries In The World - WorldAtlas.com
My own observations in the huge Brigham Young University, Harold B. Lee Library in Provo, Utah is that the library is a particularly attractive area for students to come and study, but that almost all the activity in the library is directed at computers, either those provided by the library or those brought to the library by the patrons.
The real process involves formulating research goals and then identifying the resources needed to achieve those goals. It would be very unusual to find out that I needed to travel to a remote, very large library to find exactly what I needed assuming I could not obtain the items through interlibrary loan. I am much more likely to be found looking in small, very local libraries and historical societies for the information I need rather than the huge collections in the largest libraries.
If I were working on research into English Literature, I would probably have a different perspective about which libraries I thought were "good" and which were not so good. I doubt my hypothetical interest in English Literature would take me to downtown Salt Lake City, Utah.
Despite the huge numbers of resources online, I still find myself going to the BYU Library for books and to the Provo City Library for books. I checked two books out of the Provo Library in the last week. I checked three books out of the BYU Library in the last month or so. What is important is to know when to go to the books for research. Ignoring what is readily available in your own area is always a problem.
But take consolation. If you live in some remote area and your public library is miles away and has almost no books of any interest, you can resort to the 2 billion items in the WorldCat.org catalog and find more and more of them online.