I have both and have killed deer with both. I bought them for my, then, 12 year old daughter to deer hunt with. She killed her first deer with the 30/30 and so did I.
The recoil on the 243 is less and it is a flatter shooting cartridge. Up to 150 yards or so either is great. The 30/30 shells are a bit less expensive but the 243 ammo is also relatively inexpensive.