I've used 7 mag on elk with success, and have seen several elk killed by all 3 of those chamberings. All 3 are adequate for the job. The bullet used and placement of said bullet is more important than the cartridge. Pick a good controlled expansion bullet that shoots well in your rifle. Pick something with a reputation for being tough and retaining a decent % of its weight after expansion, either in a monometal design or bonded core. Pick bullets on the heavier side of the range for their respective calibers; ex: 140 - 150 gr. in .277", 150 - 175 gr. in .284", 180 - 200+ gr. in .308".
Examples: Barnes LRX or TTSX, Hornady GMX or ELD-X, Nosler Accubond, Accubond LR or E-Tip, Trophy Bonded Bear Claw or Tip, etc.
One of our fellow OT members makes Badlands Precision Bulldozer bullets, which are an aluminum tipped monometal bullet, and they would be a good choice as well. They shoot well and are very tough.
Examples: Barnes LRX or TTSX, Hornady GMX or ELD-X, Nosler Accubond, Accubond LR or E-Tip, Trophy Bonded Bear Claw or Tip, etc.
One of our fellow OT members makes Badlands Precision Bulldozer bullets, which are an aluminum tipped monometal bullet, and they would be a good choice as well. They shoot well and are very tough.