I've stated my opinions on this on other threads, so I won't repeat myself, but I did want to say that in my view and experience, that stuff you hear about "pulling when they push", etc, is not nonsense. There is validity to it. My teacher showed us a very rare tape of Kano's (founder of Kodokan Judo) number one or two student, at age 82, tearing it up with students of all ages. None of them could throw him, and he thumped every one of them. He apparently died a year or two later, so the training didn't necessarily lengthen his life--although making it to your 80's back then was rarer than it is now--but it certainly enabled him to maintain his mobility.
Two important Japanese words in this regard are Nagare, which means flow, and Kuzushi, which means balance. In arts which base their efficacy on these things, you do progressively less and less the better you get. It's more about timing, distance, and alignment, than power and speed. This favors older folks, with skill.
It favors me, because I've done boxing, and I feel slower than a sloth on valium. I just can't pop anything fast, but I can set things up so it doesn't matter. There are a number of arts that work like this, including most forms of jiu jutsu, judo, aikido, and the stuff I do, which is technically comprised of 8 separate schools, but which I believe we are calling in sum "budo taijutsu".
I don't think Tai Chi can really be called a martial art, but I have no doubt as to its' health benefits.