Breathing is an in-built function in our organisms. It pretty much keeps on going all the time on its own unless disturbed by something. I have wondered all my life about the role it plays in our functioning. I wonder how the ancient sages would have observed the niceties of breathing and the role it plays in our organisms. It never seems me trifling or tedious to speculate how they would have found out nuances of various patterns of breathing. After prolonged meticulous observations they would have established relationships between various breathing patterns and states of mind. Then, some of them would have invented the ways to alter them to induce various states desired. Some of them would have used it as an object of meditation because it is so perspicuous a bridge between conscious and subconscious.
The incessant watchfulness of breathing can be clearly traced back to have originated in a few traditions. However, some of the most profound resources have been lost in the mysterious fog of time.
Similarly, altering the patterns in which you breathe in order to affect changes in psychology and physiology can be traced back to a few traditions.
Anapanasatti sutra of Buddha is one such source which emphasizes on being aware of breathing. This awareness ought to be unbroken and incessant. It is said that Buddha attained enlightenment by this technique. Having tried everything and having dropped everything; this technique became the final stepping stone for Buddha. This practice holds supreme importance as far as meditation techniques are concerned. You can also trace back this observance of breathing back to lord Shiva who described techniques for transcendence to his consort Parvati in Vigyan-Bhairava.
Pranayama on the other hand aims at fiddling with breath in some peculiar patterns. These patterns are clearly based on observations of Yogis. They studied various patterns of breathing accompanying various physical and mental states and based on these empirical observations and induction therefrom, they created superb science of Pranayama.
Breathing practices cannot be divided in more than these two branches. In one branch the emphasis is on watchfulness of inhalations and exhalations and the other branch stresses on both observance as well as altering of breathing. The subtle science of swara also belongs to the second branch of manipulating breathing patterns.
It must be noted that it is not possible to change the way we breathe without observing it at first. It must also be noted that there is nothing called pure witnessing of breathing-because, as soon as you start observing it—its nature changes. It is important to suggest that both of these branches inculcate some common aspects, still, they are radically different in their goals.
Pranayama, aims mainly at purging away of toxins and increasing vitality which in turn makes body ready to hold breath on its own without any effort, which in turn makes a native attain Samadhi. Anapanasatti on the other hand is a practice where meditation on breathing is an aim and it also ends up conferring state of Samadhi and not purification of body. You cannot assert that Pranayama is also meditation because you concentrate on breathing, because, there is a very tiny possibility of having sustained attention when you are continuously altering the breathing patterns. In case of Anapanasatti though, you do not disturb breathing and hence all your energy is spent in watching it and it prepares a bridge between consciousness and super-consciousness.
None of the techniques is superior over others. In various walks of life you need one technique or the other.