Theres no gun that will kill any quicker, most deer shot broadside behind the shoulder will sprint a little ways, 10 to a 100 yds with 50 being the average, I dont care what caliber you use, Ive used 7 mags and 300 mags and they sill run a little ways, no closer or farther than a .243. the only shure way to drop a deer in its tracks is a neck or head shot, high shoulder shots do it too but you ruin the shoulder meat.
Ive been using the .243 for about 30 years and my dad 20 before that, he actually went from a 308 to the .243 back in the 1960's and weve never looked back. Between him me and my brother who also uses the .243, weve killed literally hundreds of deer with it. It is very affective and will surprise you on the internal damage it does, makes soup of the lungs.
I dont care if your der weigh 400 lbs they cannot shake off the .243, many elk that go 1000 lbs have been killed with the 243. Ive shot hogs that have skin as much as 1" thick and it does nothing to stop the .243, hog skin is 10 times tougher than deers.
There are many caibers thaat are great for deer that are mild in recoil. you wouldnt go wrong with a .243, 25-06, 7mm-08, .270, .257 roberts, .250 savage, 30-30 and a bunch in between, all are affective and a deer nor you would no a diffrence.