1) Why do we create a Crystal Report on a BEx query? - Well, perhaps the business requirement is such that only Crystal Reports can do what the other tools out there cannot.
2) CR has its own advantages and disadvantages and it depends on which reporting tool you are comparing it against. But trust me, it can do almost everything, if not more, that other reporting tools combined together can do.
You might be aware that a BEx query contains metadata info which is logically arranged in the form of rows,columns and key figures.So, I did not understand "BEx query also gives the report", unless you mean that a report-like structure can be generated from BEx toolset.
The purpose of using a BO reporting tool like Crystal Reports is to take advantage of enhanced reporting capabilities like charting,cross tabs and perform complex calculations.The report can be exported to user-defined formats like excel,pdf or .rptr format(in CR 2011). It can even be fed to dashboard designer (via live-office) and a dashboard with classic look-and-feel appearance can be created out of it. Crystal Reports also supports connectivity to SAP ECC.
If your company has leveraged Business Objects Enterprise or Crystal Reports server as a BI solution, then, there is a lot more that users can do with Crystal Reports created against BEx queries. They can schedule reports,apply role-based security,create publications etc.
You might want to visit following references: