You cannot run two versions of the Remote Agent on the same system.
If you go with the older agent then you will receive a warning message when backing up from the newer BE server, that the agent is not up to date but the data is backed up as long its supported (please read the next sentence).
However any new feature or improvements in BE 20 might not be available to you if you using an old agent as certain features need a current version of the Remote Agent.
You need as well ensure that the Agent utility is configured for both BE servers and that all the "trust settings" are working fine.
You might want to consider just using the old BE server to backup the one system which is not compatible with any newer version of BE.
Everything else I would recommend you backup from the new BE server with the matching Remote Agent installed.