It is going to vary depending on your Rails application itself.
Most of these processors depend on your Rails objects will essentially load the entire Rails instance into memory. Your App memory will depend on the number of models, the impact of any plugins and the prevailing climactic conditions of your environment.
I had a 256mb Slice running several Mongrels and BackgroundRB and found that the background process used about the same memory as a Mongrel instance.
One option I have always liked is putting your scheduled logic in a Controller and calling this via Cron using wget or Curl. You get to leverage the existing Rails application and there is very little overhead in setting it up. The only reason I didn't go with this option in the above case was a requirement for hitting the queue every 5 seconds (Cron can only run every minute).