“Taoist breathing exercises are very big on NOT holding the breath and having an even in-out. Yogic breathing exercises include plenty of breath holds. Some say it helps saturate your body with oxygen. Thoughts?”
I’m all for holding the breath.
It’s a natural thing we humans can do, and in fact necessary, if you live by the water and thus obtain food by diving in such.
It’s a critical part of fitness. Although I’m not sure if the ability to hold breath has been studied and correlated as such, there are other parts of breathing such as forced lung capacity, total lung capacity and airflow that are correlated with dying less from all causes. [1-3]
These things are tough to measure without expensive machines to do so.
You know what is easy to measure? How long you can hold your breath!
Of course, it’s not just about breath-holding.
Breathing in a slow and controlled manner, which is taught inside of my new course Outside the Box Breathing, is very much related to these things. This is largely about controlling airflow.
AND the Taoists are also right…
In general, an even breathing pattern, without the use of holding the breath, is ideal.
By this I mean your DEFAULT breathing pattern, that is when you’re not specifically practicing breathing exercises.
This is a Taoist key to longevity.
In fact, this is something I talk about inside of Outside the Box Breathing. The ideal default breath is through the nose, deep but also “empty” as in not a big breath.
A tai chi master, Chris Pei, said this:
“Generally speaking, there are three levels of breathing. The first one is to breathe softly, so that a person standing next to you does not hear you breathing. The second level is to breathe softly so that you do not hear yourself breathing. And the third level is to breathe softly so that you do not feel yourself breathing.” 
There’s some deep wisdom there. And let me tell you that the third level is quite tough to obtain!
Understanding empty breathing is a key part of it. Controlling airflow is what it is all about.
The interesting catch is that specific breathing exercises that involve holding the breath and different sized legs are a useful way of getting there.
So that’s the long answer. The short answer is it is not one or the other but both in my humble opinion.
4. The Oxygen Advantage by Patrick McKeown