Can Time Machine back up different data (or different exclusion lists) to different drives?
The short answer is no, but here is why and how the exclusions work when you pick different rules for two accounts.

Whether you have one backup destination or two, the rules for multiple users is to combine the exclusions for each user with the exclusions from the system so that each user can exclude different things, but there is no "inclusion" mechanism to add something back that another user has denied.

There is a nice article on having multiple users and goes into more details on setting up multiple exclusion lists:


http://pondini.org/TM/10.html


It's not going to save backup time or space as you asked, but perhaps drives can get larger and you could just have both drives hold the same content since incremental updates mean that unless a file changes, it only gets copied once to each destination, speeding backups for subsequent backups to each individual drive when it's connected.

Pulling one drive from rotation with two works well as the system just carries on with the drive connected and then when the further out of date drive mounts again, one of the next two backups will catch it up with all changes since it was last mounted during a backup.