It's valuable to be able to share logic across client and server, especially if parts of your application are complex multi-party state machines which can be run in parallel and synchronized between client and server. At the very least it's useful to be able to share declared data structures.
Now, Node JS and Browser JS are slightly different languages, but there's enough of a common subset that you can get a fair amount of work done, especially the logical engine at the core of your application.