“In my opinion the 243 has been greatly overpraised. I consider it inferior not only to the 244-6mm Remington, but to the 250/3000 Savage which it drove from the Savage line. The handloader can get higher velocities with the same pressures in the 244 Remington case. In the 243 case, for example, the maximum load with the 90-grain bullet in the 243 is 47 grains of N04831 for 3,076 in a 22-inch barrel, whereas the 244 will handle 50 grains for over 100 foot-seconds higher velocity.
As a matter of fact, both the 6-mm cartridges were greatly overpraised when they came out, for all-around use on deer and varmints. I’d prefer the old 250/3000 to the 243 and the 257 Roberts to the 244. The reason, of course, is that heavier bullets can be used in the 25 calibers, and 90- and 100-grain bullets used in the 6mm are a bit light for the larger game, even light for brush hunting of deer.”
Jack O’Connor, The Rifle Book page 186-187
Great piece of plageristics there BigBill

While Old Jack was one of the finest writers on rifles ever he did write many years ago way before some of the powders and bullets available now. True enough better bullets are available for .257's too.
First lets go back to the question/request originaly put forth by phishroy who is a newer shooter which I must asume BigBill is too. COYOTES were the subject as I recall. Of course in true fashion we need to expell are significant knowledge gathered by others over the years whether on topic or not

Old Jack sure nuff would take a .257 over a .243 for Deer as so would most of us but then again he'd a said the .270 sure'd kick both there asses. Deer aint the isue here

Did some numbers tonight just to see how bad the .250 Sav and the Roberts kick the ass of the .243 as a coyote rifle. Bare in mind now the 6mm Rem adds a bit more velocity as the 6/284 adds even more not to mention the Gibbs or Catbird

Savage and the Roberts are by my loading manuals are one purty much the same. Here are some coyote bullet numbers for both

Sav/Roberts
75 Sierra hp @3300 100yrd zero 25.89 low @ 400
87 Hornady @ 3100 100yrd zero 26.96 low @ 400
.243 Win
55BT @ 3800 100yrd zero 17.25 low @ 400
65 VMax @ 3650 100yrd zero 19.03 low @ 400
70 BT @ 3600 100yrd zero 18.68 low @ 400
87 VMax @ 3300 100yrd zero 21.75 low @ 400
WOOOHOO the .243 sure takes an ass kick'n don't it

all those velocities are easy to make and the .243 is available in dozens of rifles not just the odd one. Brass availability, the list goes on. Sorry but there is no contest especialy if you let the 6/284 push another couple hundred fps out of those same bullets
