Choosing which version to download and install is the question of compatibility between Reportizer software and: 1) your operating system (OS); 2) other database components the application works with.
You can use Reportizer 32-bit on Windows 32-bit and Windows 64-bit, but Reportizer 64-bit should be used only on Windows 64-bit.
Let's look at a few examples...
If you want to work with dBase (.dbf) files, Reportizer can use different ways to open such files. No matter what way you choose, all involved database components (drivers, OLE DB providers, and Reportizer) have to be of the same bitness. For example, when you will work with those files through an ODBC driver, the bitness of Reportizer must match the bitness of the ODBC driver.
Similarly, if you need Reportizer to work with .accdb databases (Microsoft Access 2007 and above), the Reportizer bitness must match the bitness of the ACE OLE DB provider or Access ODBC driver depending on what component (OLE DB or ODBC) you choose.
To work with Oracle, SQL Server, PostgreSQL, Firebird, MySQL, and other server databases, the bitness of Reportizer should be the same as the bitness of the corresponding client; if you plan to work with such databases via ODBC, the bitness of Reportizer should be the same as the bitness of the corresponding ODBC driver.
And if you need to work with databases via old BDE, you should install 32-bit version of Reportizer.
Anyway, on Windows 64-bit, if you do not want to dive into these details, you can install both Reportizer (Viewer) 32-bit and 64-bit at the same time and switch between them whenever you need.