He said that both rifles are topped with Zeiss Conquest 4.5-14x44mm riflescopes. They don't get much better than that, unless you want to spend several grand.

My recommendation would be toward the .243 Winchester, since it'll likely be smaller and lighter, but if you shoot both equally, either rifle will certainly do the trick to 300 yards and beyond. I'd say that only is you go beyond 400 would the 300 be warranted over the 243. Take the one you like more. You said you want to shoot a bruiser with the .243, so I'd say go for it.

Mike