Is the Library strong in San Juan?
The Library is a strong card and it is far stronger than most of the cards that boost a single action type.  However, the Library also has disadvantages.  In the early game, you can buy a Silver mine for the same price, which can give you a massive resource advantage.  

A player must remember that the most important resource in the game is cards.  A five cost building in the early game should give an immediate advantage that will help the player get more cards in the long run.  The Library does this, but so does the Silver mine.  A good question to ask is "what am I giving up to get the Library?"

Having played the game quite a number of times, the Chapel seems to be the most important card in the game.  Most cards give you a 2:1 ratio of card costs:victory points.  The chapel gives a 1:1 ratio for three cost and can accumulate points for the entirety of the game.  The earlier you can grab a chapel, the better off you'll be.  If one player grabs a chapel early game they can run away with the game quite easily as other players find it nigh on impossible to keep up without a chapel of their own.

It is the nature of card games that some are stronger than others.  The Library is strong.  However, I've seen many wins without it.