For a long time, because I was a lefty and couldn't afford a Weatherby (or really cared to), the only rifle I owned was a Savage 110 LH in .243.
That rifle killed a bunch of deer and all but one dropped where he stood, unless you consider rolling down hill moving. The one that took off was dropped with a second shot that broke both front shoulders. When I skinned that buck out it appeared that the bullet fragmented upon impact and literally exploded just under the skin. Just a fluke. I alway shot handloads out of it and if memory serves me it was 40.5 gr of IMR4350 behind a 100 Gr Hornady bullet. I'd definately go with the .243.