This is a really good question. I had my answer all typed up once and then realized that I was contradicting myself! So I’m going to try this one more time. I was going to say that I would prefer hardcover books. However, as I was typing it out and explaining the reasoning behind my answer, I realized that I was really leaning more towards paperbacks. So I’m in a quandary here. I want to answer hardcover and paperback both! So there’s my answer: I would have both. I couldn’t choose between one or the other. Each has it’s advantages in my opinion. On the side of the paperback, they’re smaller, lighter and easier to carry around. But to defend the hardcover, I feel that they open better for me and lay in a more comfortable way (at least for me they seem to). I always struggle with brand new paperbacks; I can never get them to open far enough and have yet to manage to break the spine without tearing all the pages out! However I can also put one in my purse and read during my free time throughout the day (not really an option with a hardcover unless I was carrying around one of those gigantic purses that seem to be in style nowadays).
So I’ve probably ruined the whole point of this question, choosing one over the other. But in my perfect library, I would have both. However, I must add that I would want to have all of the books that I wanted for my personal collection (those that I would be keeping forever) in hardcover whereas the books that came and went through my shelves would be paperbacks.