It actually tells you how to view the other bug's status when yours gets marked as a duplicate of it: "The open or closed status of the original report your bug was duplicated to appears in a text box within the bug detail section of the bug reporter user interface."
i.e. in bugreport.apple.com, select your bug, then on the right detail section just under the bug title it will have a small purple text box showing the status of your bug, followed by "Duplicate of xxxxxxxx", followed by the status of the bug that yours is a duplicate of.
As it mentions, you can't view details other than the status, because the other report will probably contain private information from that person. However, you can politely request additional information about it once it's closed if there's something specific you want to know.