Yeehaw! A ballistics-which-calibre-is-adequate-thread.
Legalities aside the ballistics tables don't lie. From Chuck Hawks;
Energy of a 35 Remington shooting a 200 grain bullet at 200 yards = 841 ft. lbs
Energy of a .223 Remintion shooting a 64 grain bullet at 200 yards = 706 ft. lbs
Energy of a 30-30 Winch. shooting a 150 grain bullet at 200 yards = 858 ft. lbs
Energy of a 30-06 Springfield shooting a 165 grain bullet at 200 is twice the above choices at 1909 ft. lbs. Should also mention that some of the new Hornady bullets and loads have pushed the 30-30 over 1000 ft. lbs.
I know what I would use on a deer.....all of them (where legal). The .223 would be my last choice, but that is just me. I like to err on the side of too big than just enough. I would pack the 06.
A 35 Remington is an absolute Bambi Stomper at ranges less than 200 yards.