The file formats are exactly the same. You should have no problem going between the 32-bit and 64-bit versions unless the InDesign documents are absolutely humongous in size and complexity.
Only InDesign CC has a 64 bit version. If you install InDesign CC on a
Windows 64 bit machine you will get two versions while only the 32 bit
version will be installed on a 32 bit machine. That said, the INDD files
are EXACTLY the same.