The relative difference may very well not exist between the two scenarios. If I can't just go to the beach with my wife, if I can't go walk the dog in the farther-away park, if I can't play an online game that lasts over 40 minutes per match, if I can't schedule a music lesson - then if the above is my definition of free time, then it's going to be difficult to convince me that there's a difference between "you can't do this because you're working" and "you can't do this because you're on-call". All it takes is that I take "can't do it" seriously enough.
If your typical day-off is filled with "short" activities, if you being on-call doesn't affect plans of other people close to you, if you plan your month so that you do all the housework & chores on your on-call days, then you'll probably be OK and will testify to the huge difference between the two.
The perception of this difference will thus vary from person to person, from circumstances to circumstances, from lifestyle to lifestyle.