Having older versions of Adobe programs (most can co-exist just fine), with which one is familiar, is a good course of action. This usually allows one to continue working in the familiar versions, while they learn the new one.
Now, with Premiere, there ARE considerations about migrating Projects from older to newer versions. Sometimes, those migrations go OK, but many times they do not, and problems arise. That is why we suggest fininshing Projects in the version, in which they were started.
Things are different with Photoshop Elements, as one is only talking about Image files, which are almost completely universal.
Going back some years, I had Photoshop Version 7.0.1, and Photoshop CS on my computer, as I wanted to have my "old friend" handy, for when a client called with a deadline, and wanted the new version installed, to learn it. I also had a copy of Photoshop Version 4. installed, as it did one particular job, better than all later versions, and I had one client, who about twice per year, handed me just such a project for one of her clients. It only got used about twice per year, but made those particular jobs easy to complete, and hand-off the exact files, that the client needed.
Good luck, and newer versions of both Photoshop Elements and Premiere Elements will install in different folders, and neither will overwrite the existing version.