Use Jenkins.
Jenkins is the recent fork by the core developers of Hudson. To understand why, you need to know the history of the project. It was originally open source and supported by Sun. Like much of what Sun did, it was fairly open, but there was a bit of benign neglect. The source, trackers, website, etc. were hosted by Sun on their relatively closed java.net platform.
Then Oracle bought Sun. For various reasons Oracle has not been shy about leveraging what it perceives as its assets. Those include some control over the logistic platform of Hudson, and particularly control over the Hudson name. Many users and contributors weren’t comfortable with that and decided to leave.
So it comes down to what Hudson vs Jenkins offers. Both Oracle’s Hudson and Jenkins have the code. Hudson has Oracle and Sonatype’s corporate support and the brand. Jenkins has most of the core developers, the community, and (so far) much more actual work.
Read that post I linked up top, then read the rest of these in chronological order. For balance you can read the Hudson/Oracle take on it. It’s pretty clear to me who is playing defensive and who has real intentions for the project.