The first question to ask yourself is how much time do you have before the databases are needed again. detach/retach is great if you have the time, backup restore is great if you don't, with one caveat, any changes made after the backup will not be reflected in the new version.
So as you can see, there are different ways to accomplish what you need to be done. In a busy environment, I would generate a script of the old server and run it on the new server to place the database shell there, I'd then point all insert operations to the new server, and use SSIS to transfer all of the old data over to the new server, hopefully that will eliminate your downtime.
The key being, how much time do you have to accomplish the task, and can you do it one database at a time. If you have time, the detach/reattach method is definately the way to go, but know that the database will be down from the time you start the detach and complete the reattach. Just remember, you must factor in the time it will take to move the files from one server to the other.
An exciting time for you as it is not a routine daily DBA procedure, so take time to decide what you are comfortable with and if you have questions after the decision, post back and I'm sure many of us will gladly provide additional insight.