Both are too loud for that if you are trying to be guiet. 223 will naturally have less bark simply because there is less powder being burned though.
What kind of range are you working with?
If you want supersonic, then I think the 223 with a long barrel would be my choice, but a 300blk or similar can do it very well too.
Suppressor with subsonic ammunition would be ideal, 22lr or if you need bigger something less than 35 cal. The big bore guns just make more noise no matter what. A suppressed 300blk Bolt action with a long barrel is very quiet, AND offers good supersonic capability too. Handy gun for sure!
If a suppressor is not an option, barrel length is your friend. It makes a big difference. No muzzle brakes or porting of course.
A subsonic 22lr from a long barrel, or a pistol caliber rifle with a long barrel would be pretty quiet with subsonic ammunition. The 300blk with a long barrel again is a good choice!
HOW ABOUT A SERIOUS SUPPRESSED AIRGUN? They can be powerful and quiet. Could be ideal in the right situation. My 22pcp is a hoot...