When tapping, I have to see, or in case of watching for some event to happen to stop the time, feel/guess when exactly the distance between screen and finger approaches zero. With a stop button triggered by release however, I can just calmly rest my finger on it and raise when the event happens, without any guesswork.
"Nobody uses real stopwatches anymore" might be somewhat true, but in athletics training they still do, and it just shows that it's not possible to adequately reproduce a thing on a touch screen and have it be as functional as the real item. A stopwatch app on a phone will always be a poor substitute for a real stopwatch.
On a touch screen you have to hover your finger over the button and move it down some indeterminate distance to actuate the button. The equivalent to the above example for a touch screen is to activate on release, as you can rest in a state “ready to click” just like on a physical button that way.