You don't necessarily need both. You can use both. Google+ can backup your photos to your Gmail account. Verizon Cloud backs up to the Verizon servers.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
In principle, they are both cloud backups (backups stored on a remote server, supposedly "better" than your own local storage, more space, more redundancy, etc.
Google backups are linked to your Google account, which you can use and access from any computer, anywhere, and any Android phone/tablet/device. Your contacts, email, hangouts, photos, etc are all linkled to your Google account.
Verizon cloud stores all your PHONE information, (contacts, photos, etc) stored on the device, and is available as long as you have a Verizon account. It's more limited than a Google +/Google Drive account, and in practice and actual use, I've found it to be a bit clunky, and glitchy at times. I do usae it to backup my phone contacts, but not for photos or documents.
Windows One Drive is in the same category, only focused on Windows devices; I have a Windows computer and a live.com account; I also have a Google Drive and Google + account. They all serve generally the same purpose, and redundancy is good!
The same can be said of iTunes and iCloud for iPhones and Apple devices.
My order of preference is Google, Windows, iTunes, Verizon. YMMV