JBehave and Cucumber are completely different frameworks, although meant for the same purpose: acceptance tests. They are based around stories (JBehave) or features (Cucumber). A feature is a collection of stories, expressed from the point of view of a specific project stakeholder. In your tests, you are referring to the stories, typically via regular expression matching.
JBehave is a pure Java framework whereas Cucumber is based on Ruby. Both are very mature frameworks. You can use Cucumber from Java via the Cuke4Duke Maven plugin from Maven, but there is still a language mismatch as it continues to use Ruby internally and you will need to install this language and its infrastructure (so-called 'gems') on the machine that runs your tests. This can be brittle and the language mismatch complicates both debugging and impedes performance of your tests. There is now a pure Java implementation of Cucumber which is called Cucumber-JVM. As of December 2011, it's not released yet, but perfectly usable (edit: version 1.0.0 was released on March 27th, 2012). This new framework is very similar to JBehave as both have native JUnit support.