With either of those calibers if you put any mid-weight hunting bullet behind the shoulder it will kill the deer. Drop-dead? Yes, just maybe not in its tracks. I've only seen eight deer shot out of at least a couple hundred that I have witnessed that "dropped dead in their tracks" where they were shot. One with a .243 100 gr. Nosler Partition that I put high in the lungs and broke it's back, the next a .30-.378 Wby. with a 200 gr. Ballistic tip shot by my friend at 100 yds. in the shoulder that literally knocked it over, penetrated rib cage and never exited,we won't discuss meat damage...), a .454 Casull and a 320 gr. bullet I put through the heart at 40 yds and the deer just laid down on the spot, and 4 deer with a .30-06, the first before I was old enough to hunt that my father's friend put through an 8-point whitetail's head at 300 yds. on the run with an iron sighted Rem 760 pump, one I shot at 100 yds. facing away from me with an excellent rest on a tree that I shot in the back of the head, and two that I shot laying in their beds in the neck at 75 yds with a 165 gr. Nosler Ballistic Tip. The buck was looking at me, the doe laying next to him sleeping. I shot the buck in the neck, the doe woke up and looked around, I shot her in the neck. Neither moved from their beds, unfortunately I had to drag them through 1 1/2 miles of muddy gumbo after my stalk! The story is shot placement, shot placement, shot placement. I don't worry about dropping them in their tracks at the shot, I worry about them dropping in their tracks at some point shortly after I've hit them in the boiler room, except for the two neck shots, which were my only option. The only way you'll "drop them dead" is by taking out the central nervous system. A .243 will do it, so will a .22 LR in the right place. With a 6.5-.284 or .270 you will have not problem. Personally, I'd recommend a Nosler Partition. It opens quickly and if for some reason you pull the shot or you have a bad angle, it will run a big deer from one end to the other without question or fail, I've done it several times with a .243 100 gr. Partition as well as 165 gr. .30 partitions from .30-06 or .308.
Selmer