But patients with vocal cord paralysis on both sides are essentially faced with this very question.
Normally, the vocal cords (TVC in picture below) found in the voicebox move to accommodate talking or breathing.
When the vocal cords are apart, breathing occurs allowing air to pass unimpeded between the vocal cords and down into the lungs. However, with talking, the vocal cords come together tightly and vibrate creating voice. Watch a movie.
However, when both vocal cords become paralyzed, they neither move apart to help with breathing nor come together to assist with talking. Indeed, the voice and breathing BOTH stink.
It is in just this situation that the choice of breathing or voice becomes important because a patient can not have both. Improving one will sacrifice the other.
To explain this connection of voice and breathing further, normally, when the vocal cords are both moving fine, the voice is at 100% and breathing is at 100%. However, with bilateral paralysis, the voice and breathing are now linked to each other and collectively can not exceed 100%. As such, a patient with new onset bilateral vocal cord paralysis may start with a 40% of normal vocal quality and 60% of normal breathing ability for a total of 100%.
Using this scenario as a starting point where vocal quality is at 40% and breathing is at 60% of normal...
If a patient chooses to improve the vocal quality from 40% to 100% (an improvement of 60%), then breathing WILL correspondingly decrease 60% down to 0%... and potentially die given the ability to breathe is lost. Why? Because the vocal cords can be surgically forced together to allow for voice... but given the vocal cords are paralyzed, they can not move back apart to allow for breathing.
If a patient chooses to improve breathing quality from 60% to 100% (an improvement of 40%), then the vocal quality WILL correspondingly decrease 40% down to 0%... and lose the ability to talk. Why? Because the vocal cords can be surgically forced apart to allow for breathing... but given the vocal cords are paralyzed, they can not move back together to allow for vocal cord vibration.
The total percentage of vocal and breathing quality can never be more than 100%. If a patient wants the best possibly voice and breathing, than a compromise would be to increase the vocal quality 10% from 40% to 50%, but understanding that this 10% improvement in vocal quality WILL mean a corresponding 10% decrease in breathing ability from 60% to 50%. This 10% change means that in the end, the voice and breathing would both end up at 50% of normal.
In most cases of bilateral vocal cord paralysis, it is the reduced breathing and shortness of breath that bothers people the most. The voice isn't good, but when given the choice, most people choose to try and improve their breathing ability understanding their voice may further deteriorate.
To read more about such treatment options, click here.