"The 357 from a rifle is snapping at the heels of a 30/30."
Comparisons taken from the 12th edition of Cartridges of the World.
.357 magnum 158 grn bullet typical pistol load velocity of 1200 f.p.s. producing 505 ft/lb of energy at the muzzle.
.357 magnum 158 grn bullet 20-24" rifle barrel velocity of 1650 f.p.s. producing 955 ft/lb of energy at the muzzle.
.357 magnum 158 grn bullet 20-24" rifle barrel velocity of 2000 f.p.s. producing 1403 ft/lb of energy at the muzzle.
.30-30 Winchester 150 grn bullet velocity of 2450 f.p.s. and producing 1995 ft/lb of energy at the muzzle.
A difference of 592 ft/lb of energy between the hottest .357magnum load in rifle and a standard .30-30 load isn't exactly snapping at the heels in my view.
I'm not even remotely suggesting that a .357 can't kill deer because it can and often does elsewhere, but it doesn't even come close to achieving the required energy levels in England and Wales for larger deer species. So given the choice between a .357 rifle and a .243 rifle I would stick to the .243win.
P.S. Just to indicate that I not prejudiced against pistol calibre rifles, I've owned three .357mag rifles previously, and also a .44mag rifle that was approved for stalking. The .44mag was clearly the better cartridge but I never became a huge fan of under levers despite using them a fair bit for the best part of ten years.