Respectfully, I don't think I've done what you say I've done. I say "they're not the same thing" because, as I said in the post, a lot of people lump them together as "investing in knowledge for society" or the like.
I didn't set out to identify a library's strengths. I believe many of the university's supposed strengths are actually better applicable to libraries.
It's all about one's point of view. I'm assuming you're out of college and don't care about the cost of tuition. A college student couldn't care less about public libraries because...
1. Colleges have their own libraries
2. Cost of tuition is way more important to him/her
From my point of view, it looks like this:
How much information is in a library that can't be found elsewhere online? Now what about the other way around, though. How well can advanced college topics be taught with a book from a library?
I'm not sure if universities should have their funding cut but libraries seem very foolish to keep funding. Wouldn't it be better to invest all the money currently spent on libraries in to an online library? Imagine the amount of information we could have easy access to?
The top story on Hacker News right now, http://news.ycombinator.com/item?id=3607217 (also the link I start the post with), explains one of the problems with doing that. As many important functions move online, the library is one place someone without a computer and computer skills can use to gain access to the online world.
Libraries also provide a meeting place for the community, access to librarians, and many free classes.
I do agree it makes less sense now for libraries to have large physical collections. The shift to an online library seems inevitable there. But access to this from local libraries is still important.
I didn't set out to identify a library's strengths. I believe many of the university's supposed strengths are actually better applicable to libraries.