If the only thing we're evaluating is the cartridge, then I might lean toward the 6mm Remington for the longer neck and sharper shoulder. Also, I don't care what cartridge the head stamp says, so I buy Lapua, Norma, or RWS 7x57 or 8x57. That requires annealing and neck turning but the availability of 243Win brass doesn't come into play for me personally.
All that said, I have really hard time recommending the 6mm Remington over a 243Win, or the cartridge you left off, 6mm Creedmore, for 95% of people. All three are almost identical for practical purposes. Factory rifles and ammo are more abundant in 243Win and probably 6mm Creedmore. If you want to use a 700 S/A the 6mm Remington can be a pain, although it should fit better in most clones as well as probably a number of medium length actions.
For whitetails I'd say almost any bullet 85-105gr would be great from any of the three.