From the Jenkins website, http://jenkins-ci.org, the following sums it up.
In a nutshell Jenkins CI is the leading open-source continuous integration server. Built with Java, it provides over 300 plugins to support building and testing virtually any project.
Oracle now owns the Hudson trademark, but has licensed it under the Eclipse EPL. Jenkins is on the MIT license. Both Hudson and Jenkins are open-source. Based on the combination of who you work for and personal preference for open-source, the decision is straightforward IMHO.
Hope this was helpful.