The .243 round is not only slightly larger calibre than the .22, but a considerably longer bullet with a hugely more powerful propellant. Compare the Wikipedia pages:
http://en.wikipedia.org/wiki/.243_Winchester
http://en.wikipedia.org/wiki/.22_Long_Rifle
In muzzle energy terms, .243 delivers between 8 and 20 times the energy; the bullet is more aerodynamic so more stable at increased ranges, with a flatter trajectory. That doesn't mean the .22LR cannot be lethal- in fact it can kill at far longer distances than it is accurate- but it cannot be relied on.