What do you like best?
Hudson has been a solid continuous integration, continuous delivery, continuous build and automation tool for years. It's hard to fault. It works, it's free, easy to install and works amazing with Java.
If you there was no Jenkins, Hudson would be a no brainer to use.
What do you dislike?
It's not Jenkins. After the fork and the split with the open source community, Hudson has not gotten the tools, support or community it once had. At this point, it's probably compatible with Jenkins for the most part, but I am not sure if it's fully compatible.
Recommendations to others considering the product
Don't use Hudson, Oracle's license made it fork into Jenkins. All new support, tools and users are using Jenkins.
Hudson really lost it's steam.
What business problems are you solving with the product? What benefits have you realized?
To easily run builds, tests, deploys and everything else you can think to run. Runs it via schedule, github, SVN, web api and a ton of other things. Great for building maven, sbt, gradle and a ton of other things. Runs your tests and publishes the results. It can be monitored from a number of little watcher tools