They become geriatric at the same time we do, but their advancements have made geriatric living better and last longer
...Yet the show makes some attempt to show that Jean-Luc Picard is a decade older than Patrick Stewart, and physically very fit even for somebody who'd be Stewart's age today.
McCoy was two feet, one arm and four fingers into grave in "Farpoint" at 137, but does that mean he was doing extremely well for somebody his age, or extremely poorly? He has lived a demanding life, and his body has been violated by all possible and impossible ailments. Perhaps somebody like wiry Admiral Chekote is a better example of a 130+-yr-old in the 24th century?
Certainly O'Brien's comment about wanting to die at 150 establishes that this is a rarely (if ever) achieved age in the 24th century, as obviously the Chief isn't in a hurry to leave.