REST is almost always going to be faster. The main advantage of SOAP is that it provides a mechanism for services to describe themselves to clients, and to advertise their existence.
REST is much more lightweight and can be implemented using almost any tool, leading to lower bandwidth and shorter learning curve. However, the clients have to know what to send and what to expect.
In general, When you're publishing an API to the outside world that is either complex or likely to change, SOAP will be more useful. Other than that, REST is usually the better option.
The acronym REST stands for Representational State Transfer, this basically means that each unique URL is a representation of some object. You can get the contents of that object using an HTTP GET, to delete it, you then might use a POST, PUT, or DELETE to modify the object (in practice most of the services use a POST for this).
