Office 2016 which comes with Office 365 is great, and has some excellent new features. However there is a catch for people that may also have a copy of Project or Visio that is not part of Office 365 (ie and “old school” licence was purchased). The trap is you can’t run both Office 206 which is part of Office 365 and an older version of Project or Visio together. The only way to get them to work together is to purchase a subscription copy of Project or Visio.
Technically Office 365 uses a technology used “Click to Run” this won’t operate with Office software installed in a different manner, ie you purchased a disk or downloaded. More technical details are available here
What are your options?
Write off your investment in Project or Visio and purchase a new subscription
Keep using Office 2013 if you are already using Office 365. Read the discussion here on how to install Office 2013 Click to run and stop it upgrading
Current timeframes indicate that Office 2016 will start to be automatically installed and upgraded for Office 365 users in February, unless you delay it. Updates for Office 2013 as part of Office 365 will stop in September 2016.