There are multiple options for fetching data on run time using Connect Web Service for an addin.Which option is faster between Object query language and Report execution using Rightnow Connect ? What are the pros and cons of both approaches ?

  

ROQL supports QueryObject which returns a representation of the object, and QueryCSV which returns tabular data which more closely resembles report execution. So it depends on your need that whether you requires Objects or tabular data.

If it is tabular data both ROQL and reports do effectively the same work and performance mainly depends on the join within the tables.

You should use ROQl a) if your work can be done with objects that exist in the CCOM. b) The benefit of ROQL is that it is a managed framework. This means that your queries will continue to work even if the underlying schema changes.

You Should use reports if you need access to tables that are not yet exposed in the CCOM.