The verbiage would be different and, in the member's mind, they may not even know they got unsubscribed so would confuse them to get an invite to a group they are already in.
Also, no subsequent welcome message.
But could coalesce both suggestions into single email - either link or reply would resubscribe.
Was thinking that having From: be the owner/mod sender would avoid message going into spam folder.
Another thought - email containing many links is sometimes considered "spammy" so email with no links might be better.