Stackoverlow decided to use OpenID probably due to its simplicity while others believe that Information Cards (e.g. cardspace) is a better strategy in that it is backed by major industry vendors and is known to be more secure.
Are there libraries that a developer can drop into a Java web application that will easily support both?
Here is a presentation that compares the two. There is even a link at the end for Java implementations of CardSpace. However, it seems to be from a CardSpace point of view, so be careful of bias.
Information Cards and OpenID are not mutually exclusive, and can be used to great effect in a complimentary fashion, as demonstrated in this short video by Kim Cameron from his Identity Weblog.