Death from thirst is quicker. A really rough rule of thumb is that a person can live for three minutes without oxygen, three days without water, and three weeks without food.
It is a little easier for the body to compensate for not eating vs. not drinking. The body can burn fat and muscle to create energy. The body can't make more fluid on its own if none is coming in.
As an EMT I would guess that you'd have more dramatic physical consequences from dying of thirst. When a person is severely dehydrated, there isn't enough fluid in the body to carry blood and nutrients around or to maintain an adequate blood pressure. Eventually you'd be unable to stand up without passing out (you wouldn't have enough blood pressure to fight gravity and reach the brain). And eventually you'd go into hypovolemic shock because there isn't enough fluid in the body to reach the brain and other vital organs. Severe dehydration can also injure the kidneys, and without the kidneys to filter out the stuff your body doesn't want, all those toxins stay in the body. In cases of kidney failure, people can drown in their own body fluid because the kidneys aren't getting rid of fluid so it builds up in the lungs. Plus the toxins that we normally pee out remain in the body, gradually the blood becomes more acidic, and that affects the brain and other parts of the body.
OTOH, I used to work in hospice, and when people were close to death and wanted to die on their own terms, they often would stop drinking and eating. I'm told that towards the end it's peaceful, sometimes even euphoric at the very end.
But those were people who were already very close to death. I can tell you that because of a medical condition, I once went a year eating approximately once every two days. My body was literally starving and it sure as hell let me know. My brain was constantly screaming at me “EAT SOMETHING NOW OR YOU WILL DIE!!!” For a healthy person to die of either thirst or hunger, I’d think they would constantly be in anxiety/panic mode, aside from all the medical problems it would cause.
