I would say that Report Designer (Visual Studio) is aimed at developers who have a version of Visual Studio, while the report builder is aimed at non-developers who are familiar with Office applications, who just need to let ClickOnce install the report builder (but developers can use him too).
The report designer has fewer functions, but you can still do a lot with it, so it can be useful when you need to quickly adjust the report, and you need more time to do this using the Report Designer.
Having said that, the following scenario is perfectly valid:
- Create Report in Report Designer
- Expand Report
- Make a fix with Report Builder
- Save report (= expands report)
Here are the official descriptions of each environment:
Report Designer
The report designer in Business Intelligence Development Studio is a reporting development environment hosted by Microsoft Visual Studio. Use the Project Designer project and solution files to organize and save a master copy of report definitions, report parts, shared data sources, shared data sets and resource files such as images and ESRI shapefiles for maps.
report builder
Report Builder is a reporting development environment for business users who prefer to work in a Microsoft Office environment. You work with one report at a time. You can change the published report directly from the report server. You can quickly create a report by adding items from the Report Parts Gallery provided by the report developers from your organization.
Additional information on the differences between Report Designer and Report Builder: