Can I swap C4D files between different versions if I'm on subscription?

In most cases, yes you can.

Important Notes:

• Files created in Cinema 4D 11.5 or older can not be opened in R20 and newer. To open these files in R20 or newer you must first save the project in version R12-R19, then you can open the C4D file in R20 or newer.
• New features added in future versions may cause a "Missing plugin" error if the C4D file is opened in an older version that does not include those features.