MS Project Server has all the features that MS Project has, but has the following additional features:
- Portfolio management: Ability to manage and track project portfolios (apparently it has intelligent decision making for project selection and prioritization)
- Collaboration: Because MS Project Server is built on top of MS Project Server, then it has all the collaboration for features of the latter.
MS Project has a huge official and unofficial community, and it's very easy to use, and it's relatively inexpensive. MS Project Server is ideal for large companies managing several portfolios of projects.
Clearly you won't need (the complexity nor the price of ) MS Project Server if you work on a small project in a small company, but for companies with a PPM, then a MS Project Server is a better choice.