Why the implied either/or? Why not do both meditation and exercise?
Often when you hear of great athletes, especially great endurance athletes like Michael Phelps, they talk about how they don't think about the whole X meters or Y miles at once. They focus on performing the next stroke or next step or next pump of the pedal perfectly. This to me, as a layman, sounds similar to the idea of focusing on the next breath as is a common practice during some types of meditation.
When I used to meditate I used to like to let my mind wander, then focus on breathing. Or vice versa. And many people prefer guided meditations.
As there are so many types of meditation I do not see any reason to believe that some types might overlap with exercise quite comfortably. Guided meditations might be more difficult because it would presumably be harder to both focus on the next stroke and focus on the meditation, and I guess that goes as well for the wandering mind meditation (you really don't want to run absentmindedly in NYC where I live, maybe in the country or even suburbia it would be more feasible).
Anyways, I guess to me it doesn't seem like it has to be an either or but could be one activity. If Siddhartha can do it, so can we :-).
I should start running again though, that's great exercise!
I'm no expert but I think concentration is only part of the picture. This can be concentration on the breath, or concentration on a physical activity as you describe it. The other part is using the highly developed concentration state for the actual (mindfulness) meditation, which is pretty hard if you're moving around, at least for a beginner.
I'm talking about Vipassana practice, which is all I know about. As you say there are many forms of meditation.
edit: I used the word 'deliberate'. I should say seemingly deliberate. To be exact, it's not about deliberation or thinking at all.
Intense competitive athletics is certainly conducive to focus that is likely similar to meditation. One book that I found somehow helpful or comforting was http://www.amazon.com/Zen-Art-Archery-Eugen-Herrigel/dp/0375.... I found myself following similar practices, by which I mean I would approach the barbell, get set up, and then wait until my body spontaneously performs the lift.