One of the most common questions I am asked is what's the difference between Microsoft Project and Project Online. Which one do you need? Do you need both?
One big difference is the number of projects you're managing. If you're managing one project at a time, and you don't have a lot people accessing the project, then Microsoft Project is probably a good fit.
If you're managing multiple projects (or have multiple project managers managing projects) and the entire team needs to access the project then Project Online might be a better fit.
Another contributing factor is price and preference. Since Project Online is subscription only, you pay a monthly fee. With Microsoft Project, you can either pay a monthly subscription fee, or purchase a license. If you go the license route, anyone wanting to view the project would need a license of Project installed on their computer, which can get pricey.
And a heads up to my Mac friends... currently Microsoft Project can only be installed on Windows. But you can use Project Online with most of the same functionality.