Hum, there is no trick at all in fact, you install one version (32 or 64 bit, doesn't seems to matter), you install the other version in a different directrory (I choosed "Vue 6 xStream 32" and "Vue 6 xStream 64" for names) and that's all :)
You only need to enter your serial and activation code once, and I think it's also perfectly legal (at least I hope so, I doubt there would be any objection to this from e-on since apparently they provided the needed support in Vue)
Your Vue 6 xStream.reg file will contain two entries :
VueFolderPath32:D:3DVue 6 xStream 32 and VueFolderPath64:D:3DVue 6 xStream 64
If you customized your installation path for the content, when installing your second version, it will by default offer to use the same path, allowing you to share the content between the two versions installed

Ab :)