While it is true that these two forms of exercise do wonders for the connection between movement and concentration of the muscles during a workout, Dr. Jim Gavin brings up a great point in his article on Mindful Exercise.
Dr. Gavin argues in favor of what he calls the body-mind cube, discussing ways to incorporate focus and consciousness in the commonly categorized body-mind exercise into all forms of exercise. Dr. Gavin breaks down mindful exercise sessions into three elements and transfers them to his cube technique (you can read the details here).
To summarize, every exerciser, regardless of the exercise they are participating in and what fitness level they are at, can make an activity mindful:
1.) Focus on Breathing
2.) Focus on the muscle you are engaging for the movement
3.) Leave the rest of the day at the door
I understand that number 3 is the most difficult by far. However, a completely focused, intensely engaged muscle focused and even breathing session will give you that truly mindful exercise experience.
So next time you head to the gym, track, or weight room leave your to-do lists, plans, kids, friends, family, etc. out of your session!