I use Sharepoint for managing projects all the time, but it is very different to MS Project. Sharepoint gives me lots of freeform lists and tables that allow me to manage things like incoming information, issued documents, reports being prepared, refeneces, risk assessments etc. You can configure views to give you some basic information like how many comments still need to be addressed, what is the current status of xxxx etc. As a project management tool it can therefore manage the whole process.
MS Project is suited to planning a project in terms of time and resource and then monitoring the projects progress against that plan. This gives it a very different emphasis compared with Sharepoint. It is more suited to managing larger projects with specific time and resource constraints and lots of complex interactions. It doesn't necesserily help manage a project, it is more of a planning and monitoring tool.
Which one to plump for very much depends on how you would like to manage a project but I wouldn't say that either is mutually exlclusive. They both achieve different things, but you can also acheive the basics of either using other less sophisticated approaches.