I know that Java's standard library is very complete. I know very little about Go's, but I presume that it's not more complete than Java's. Is Go's library easier to use than Java's? Is it significantly easier?

Go is through it's integrated support goroutines (green-threads) very efficient at IO, while still presenting it in a traditional fashion (like blocking IO).

Java can also be very efficient, but only provides the lower level NIO library out of the box. To use that you either have to build und understand a lot of components for yourself (e.g. an IO Reactor, timer handling, etc.) or include one of the bigger frameworks for this purpose (e.g. Netty).