@ 10:24 am (GMT)
Caleb MayfieldBrendan, to be truly discreet you need the bullet to be traveling at subsonic speeds as it leaves the suppressor. So for comparison, the 223 is still going to have a loud crack from the supersonic projectile.
If it were me I think I would ask the following questions:
How far am I going to be shooting rabbits?
Do I want anything to be left after shooting them?
How quiet do I need to be? (Houses nearby or just don't startle the horses?)
What subsonic ammunition is available for either option?
What is behind the rabbits mostly? Are ricochets a concern?
I favor a 22 LR shooting subsonic ammo as it is for almost all my small game hunting. I'm currently working on a custom stock for my Savage Mark II to give me better results in long range shooting. From shooting this rifle with the factory stock I can tell you I would have no reservations about shooting rabbits at 200 yards from a good vantage point. If the new stock and bedding job prove to be as effective as I hope, I believe the could push to 275. Beyond that I have had difficulty maintaining predictable groups under 4".
If I were treating rabbit control like pest control with no intention of eating anything left, and the supersonic crack of the bullet is quiet enough to not disturb your hunting environment, I would go with the 223 and work up a bunch of highly frangible rounds to make sure that the bullet doesn't travel beyond my target.
That's my thoughts. I hope it helps.