There are two concerns I see with the person who waits an extra ten years before becoming active.
Sensitive Ages for Athletic Attributes
In his book Science of Sports Training, Tom Kurz goes into several pages of detail on how to maximize the potential of an athlete by matching their age-related susceptibility to certain kinds of development with the appropriate training. As he describes on pages 303 to 304:
At different ages children and youth are most receptive to different stimuli developing different movement abilities. These are so-called "sensitive ages" for a given physical ability (endurance, speed, strength, flexibility, components of coordination). The consequence of not developing a given ability during its sensitive age is reduced fitness and athletic potential lost forever (Drabik 1996).
Specifically, this will determine each individual's ability to realize their maximum lifetime potential in specific types of athletics. From page 305:
In gymnastics, figure skating, and swimming, [the age of maximum realization of the athlete's potential] is between 14 and 20 years. In weightlifting, track-and-field throws, and long-distance running it is between 21 and 30 years. In other sports this age is between 18 and 26 years. These ages are relatively stable, determined by regularities of human growth and maturing, and are not influenced much by the time of starting sports nor by the system of training.
So regardless of other factors, the person who starts working out in their 20s will have the chance to reach their maximum potential, whereas the person who waits will have missed the boat on some specific avenues of maximum athletic potential.
Long-Term Effects of Being Sedentary
There are thousands of studies going into the long-term effects of being inactive. Rippetoe and Kilgore put it best on page 2 of Starting Strength:
Humans are not physically normal in the absence of hard physical effort.
Without running games, carrying and climbing things, random play, contests and sport, people wither. They atrophy in a number of ways too great to detail here. They roll the dice with cancer and heart disease. Their body becomes used to inactivity in its metabolism and its mind, making changes later in life to diet and exercise habits harder.
I could cite studies that talk about the occlusion of arteries and the long-term effects of sitting, but I think we're all clear that there are real health consequences to being inactive for ten years. Perhaps one can mitigate those negative effects by turning their habits around, but it's like smoking: you do immediate good by quitting, but reversing the damage takes a long time. Sometimes it takes longer than you have left.