Up front .. I am a Hudson committer and author of the Hudson book, but I was not involved in the whole split of the projects.
In any case here is my advice:
Check out both and see what fits your needs better.
Hudson is going to complete the migration to be a top level Eclipse projects later this year and has gotten a whole bunch of full time developers, QA and others working on the project. It is still going strong and has a lot of users and with being the default CI server at Eclipse it will continue to serve the needs of many Java developers. Looking at the roadmap and plans for the future you can see that after the Maven 3 integration accomplished with the 2.1.0 release a whole bunch of other interesting feature are ahead.
http://www.eclipse.org/hudson
Jenkins on the other side has won over many original Hudson users and has a large user community across multiple technologies and also has a whole bunch of developers working on it.
At this stage both CI servers are great tools to use and depending on your needs in terms of technology to integrate with one or the other might be better. Both products are available as open source and you can get commercial support from various companies for both.
In any case .. if you are not using a CI server yet.. start now with either of them and you will see huge benefits.
Update Jan 2013: After a long process of IP cleanup and further improvements Hudson 3.0 as the first Eclipse foundation approved release is now available.