Varmint loads to tend to result in fairly short barrel life in the 243 - i think 2000 is about the point where you start to notice accuracy deteriorating when you use one as a varminter. The guys who use them for punching paper often talk about barrels going around the 1500 round mark, but they are running very hot loads and really obsess with the minutiae of precision. But in a long range varmint gun like a 243, a small loss in accuracy rapidly becomes significant. Deer hunting accuracy will be maintained for thousands more rounds. You can stretch barrel life by using more mild loads and using heavier bullets moving more slowly - it is light bullets being pushed fast that kills 243 barrels young.
If i wanted a 6mm for small deer and varmints, i'd be thinking 6XC, now that Norma has standardised it. The 6mmBR and improved versions thereof would also have to be considered, but can be difficult to get feeding reliably.