Hi Sujoy,
Cucumber and JBehave are designed to solve the same problem: writing automated tests in a way that they feel approachable to non-technical project stakeholders.
I've never used JBehave, but my understanding is that where Cucumber differs from JBehave is in how specifications are written. They both use plain-text files, but Cucumber uses the Gherkin syntax for its feature files, which is getting quite wide adoption, with tools like
http://www.relishapp.com being written to publish feature files, for example. There are also tools to run Gherkin tests in various different languages such as SpecFlow for C#.
I don't know about the relative merits of the two tools, so I can't comment on that I'm afraid.
To be honest, I'd say that the main thing is not which tool you use, but how you use it:
- are you having regular sessions with the non-technical team members to review the scenarios you're working on?
- does everyone on the team have easy access to the scenarios?
- does everyone on the team feel a sense of shared ownership over the scenarios?
If you've achieved that with JBehave, I'd say you're doing just fine.