At the moment all Power Ports are Global in nature. Where this becomes an issue is with trying to use Hierarchical sheets to simplify the design in Eeschema.
Here is a single screen grab:
At the moment, to have +3.3V_2 on sheet 2, the hierarchical sheet has to point to a seperate file. One of the benefits of using hierarchical sheets is that they can point to a single file and only one file needs to be altered to make the rest of them the same; except for Power Ports (and maybe something else I don’t know about).
As can be seen below, using separate files for each hierarchical Power Port does allow for the visual representation of the Power Ports that I was expecting. However, each individual sheet must be manually edited to match the other sheets.
At the moment, I typically use a text editor to copy the first hierarchiacal sheet then edit the Power Port symbol names on following sheets.
I hope that others are willing to help work through any potential issues before I finally create an account and actually upload this idea to the bugtracker/wishlist webpage.