150 yards?!
I really hate these various incarnations of caliber wars threads.
http://www.youtube.com/watch?v=hY0w1c-gf18
The 243 fails as an elk round exactly the same way that a .308 or 375H&H magnum fails, by not hitting the important stuff.
Unrecovered animals are not evidence of a failure of the bullet. They're unrecovered. We don't KNOW where the bullet hit. Interestingly, recovered animals always have holes in the important stuff. It should lead one to believe that poking holes in the important stuff kills things and when things don't get dead, it's because the important things didn't get holes poked in them.
Young people, small-framed women and other with an aversion to recoil regularly hunt elk with the 243. It does the job when they do.