You need a 32-bit JVM to use 32-bit Eclipse, and you need a 64-bit JVM to use 64-bit Eclipse.
Please note that the 32-bit JVM can run on a 64-bit OS. I have a 64-bit version of Windows 7 with 32-bit and 64-bit JVMs installed. I sometimes have to edit the eclipse.ini file to make sure that the correct JVM is selected.
There are no differences in compatibility with workspaces between 32-bit / 64-bit variants of the same version. The native bits, which are 32-bit / 64-bit, are for the built-in interface and file system integration.
If you are using a 64-bit OS, you should use the 64-bit JVM / Eclipse. This avoids many memory problems that can lead to 32-bit installations. For example, often a 32-bit JVM / Eclipse does not start with -Xmx1024m due to fragmentation of the address space.
Eclipse's 32-bit builds are still in production because there are still quite a lot of 32-bit OSs.
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