Both are running the same OS build (14393.726) and app version
(16.1118.10000.0) and are fully up-to-date. Is there something that
determines which editing tools are used? And how can I get the same
version on both (ideally the older version)?
Based on the article: New features arrive in Microsoft Photos on Windows 10
It appears while the new interface for Microsoft Photos is completed it still is being slowly pushed out to users. I base my conclusion, based on the fact they are still collecting feedback, as stated in the following statement by Microsoft
We’re making a big investment in Photos these days and we want your
feedback on how to make it better. You are a key part of all the
changes we make to the Photos experience. Try out the latest update,
edit some photos, draw on some videos, and continue to share your
feedback with us through the built-in feedback tool. You can find
“Send Feedback” under the “…” menu.
It is worth pointing out the article was lasted updated on January 19, 2017 2:43 pm.
So the simplest solution is to just uninstall and reinstall it. I have confirmed when you do this, the notification that explains the look has changed, appears again.
It appears that, in order to have the ability to uninstall the Photos application, you have to use StartIsBack. Once you have it installed, you can uninstall the Photo application, by selecting uninstall. Once you have it uninstalled you can uninstall StartIsBack.
You can initiate the installation process, by going to the Microsoft Photos, application page. You can also locate it in the Store and simply install it.
Once the application is installed and you launch, the following notification, should be displayed.