Which style should be used? Is one better than the other?
The choice of REST versus SOAP is nothing more than a choice over a design strategy that is based on business and application need, but it is a choice that can profoundly impact how an application is used and evolves over time.
Where both SOAP-based web services and REST-based web services are offered,
REST-based APIs are more widely used, mainly because REST services are easily used from scripting languages, in addition to easily allowing for browser-based experimentation.
In summary, the answer is not an either/or proposition. It is perfectly okay to have both types, depending on the problem that must be solved. You might want to provide REST web services for Web 2.0 and browser-based clients, or you might want to use SOAP web services if the architecture must address complex requirements that are addressed by SOAP-based web service standards, such as transactions, security, addressing, trust, and coordination, which REST cannot provide or requires work to implement in REST.