The .22-250 has much higher muzzle velocity, like 4000 fps were as a .223 is less than 2000 fps.
I have 2 223 rifles and hum neither of them shoot below 2000 fps not sure where you are getting your info from. But it is slightly off.
If a 223 can kill terrorist it can kill a deer. Proper bullet and SHOT PLACEMENT is KEY.
I have a Varmint load in my 223 that is scooting along at 3600fps.
Using a good 60 gr Nosler Partition bullet suitable for deer sized game.
please visit hodgdon.com and look up the loads.
Again proper bullet and proper shot placement is key with any cartridge. You don't need a Magnum to kill a deer.