You can’t really compare these as they are different products. Project is a key component, along with Project Server, in an EPM solution. If you use Project connected to Project Server you still use Project to plan your schedules (so you get all of the features of Project), but you now use Enterprise resources (you can still use local resources but generally they are not used), plans are saved centrally, visibility of all the projects are available via IE, reporting is via Excel Services (and others). From a PM’s perspective the scheduling benefits of using Project connected to Project Server are minimal; from a resourcing perspective you can see each resources’ assignments across all projects.
I can only think of one downside – versions – only a single version of any project can be saved to Project Server.