I have and use both, but the 223 and 204 get the most use. push the right bullets and they flat out kill coyotes. I ran my 204 for years, got tired of lugging a heavy barrel around and got a light 223. I have killed coyotes past 500 yards with the 204. I shot one at a rangefined 394 a few years ago, right through both shoulders, the 39 blitzking went in and didn't exit, very impressive diameter wound channel and a small 19 gr mushroom under the hide far side. I have tried the 39 gr berger and find its bc too low for longer shots in open country. shot a fox at 410 and it never opened. ice pick wound in and out, its low bc causes it to slow down fast. great bullet at shorter ranges though, 250 and down, if the wind is not howling.
in the 223 I push a 1365 sierra. shot a big male with a frontal shot few weeks ago, hit one shoulder, dug after the bullet, found the jacket 16 inches in. great penetration, exactly what the 1365 is known for.
my advise get a 223 first, and a 243 later on. the 243 is great all around gun.