I had a 6MM Rem. for years and wish I had it back! I consider the .243/6MM to be the minimum for deer, but a great minimum they are!
If I were buying another one today, it would be the .243. The 6MM hold only about 100 FPS advantage over the .243, so the difference would be in ammo availability! You will find 10 times the selection in .243 that you will in 6MM!
That, coupled with the fact that the .243 is a short action round, tips the scale in favor of the .243.
The .243 and the 6MM are both the same bullets in different cartridges.
The 6MM Rem. got its start in life as the .244 Remington. Because of rifle twist rate, the .244 Remington was not as accurate as the .243 Winchester. Remington discontinued the .244, and came back out with the 6MM Remington, which with a better twist ratio, it was every bit as good as the .243's! But alas, with the bad reputation that it started life with, the 6MM Rem. never caught up to the popularity of the .243 Win.