Geoprocessing services are not a big part of BA Server. The functionality that is available with BA Server that is not available with ArcGIS Server is focused on the reporting aspect. We allow reporting against our data and against a user's own data if they wish. Some of the other functionality that we provide, beyond what ArcGIS Server provides, allows users to setup customer and store layers and associated these layers with each other, perform segmentation analysis.
A good reference to sget an idea of what the BA Server specific tasks are and what they do is the BA Server REST Reference Guide. You will not be able to run requests from the documentation without BA Server installed on your local machine, but there are illustrations in the documentation.