Installing v.15 will create a folder in C:\Program Files (x86)\Toon Boom Animation\Toon Boom Harmony 15.0 Premium (Windows). This will not be written over the previous version installed at C:\Program Files (x86)\Toon Boom Animation\Toon Boom Harmony 14.0 Premium. The same applies to your preferences that will be in C:\Users[User]\AppData\Roaming\Toon Boom Animation\Toon Boom Harmony Premium. Inside this folder you can have folders for different versions, such as full-1500-pref and full-1400-pref. (For Mac: /Users/[user_name]/Library/Preferences/Toon Boom Animation/Toon Boom Harmony Premium/)
You can open files made with previous versions so it might not be particularly useful to keep both versions installed. But if, for instance, you have v.15 but have a collaboration with someone or a studio that works with older versions you should have whatever version they’re using installed. The most recent license should work with older installs, but you might need to have Gold Support since technically you’ll need it to have access to previous versions.