Athletically, it does pay to be young in general, but you also improve certain things and make your life easier with what they call “training age.”
Take the example of “dad strength.” “Growing up,” writes Dan John, “a lot of us used to lift weights all the time but still could not torque a wrench or open a jar like dad, who never did any lifting.” By 16 I was bigger than my skinny dad and much stronger with a barbell, but it was another decade before I was better at moving a refrigerator. Dad had spent half a lifetime playing sports, loading moving trucks, and manhandling boxes down from the attic.
In real-world strength tasks, dad was stronger because he had an extra 30+ years of “training age.” With all that experience of moving everyday stuff around, he was just really good at it. Folks underestimate how much strength is a skill, the sum of a dozen mundane little variables of balance, posture, breathing, timing, and the use of your abs. Especially the abs. (As Pavel Tsatsouline says, strong abs + strong grip = strong person. Everything else is icing on top.)
With training age you can also get another huge asset: tendon and ligament strength. Even with little training, most of us already have good strong muscles. Our weak link is the thin little tendons that hold our big muscles onto the bone. (Think of eating drumstricks. Those little white plasticy cords that hold the meat onto the bone? Those are tendons.) Tendons are weak and vulnerable, and your muscles are already so strong that you could accidentally tear them off the bone, and then you’re in big trouble. So your body protects you by turning your muscles off if they get too close to overloading your tendons.

And it’s hard to thicken and strengthen your tendons. They receive little blood flow, unlike your muscles. So to grow them you need years of stimulus. In other words, you need years of training age! If you’ve handled heavy things routinely over many years, you’ve gradually grown and toughened those tendons and ligaments and so you can exert more muscular strength before your body gets worried and shuts the muscles down. (Incidentally, this is a problem with steroids: they build muscles faster but not the tendons and make it easier to “blow a tendon,” usually in a pec or bicep.)

Sometimes you meet retired athletes who have not trained in years and have average-guy muscles, but they can still do freakish feats of strength because under the skin they still have those Superman tendons. And because your strength depends so much on skill and tough tendons, which depend a lot on training age, strength ages really well. Powerlifters may not peak until their early 40s, for example, and they can retain much of their strength even if they stop training and regain it quickly when they resume.
Of course, you do not improve every attribute with training age, or all the Olympic medals would go home with the silver foxes. You lose some joint elasticity and aerobic capacity every year that you are alive, for example, and though you can mitigate that with training, you can’t reverse it. But if you are a lifelong athlete or laborer, then depending on your sport you may find yourself with relative advantages that you can play to.
I’m 58 and pretty strong, but I can carry sandbags and awkward objects better than many younger, stronger guys.