If you wrongly convict someone and put him in prison, you can always compensate him for the time served/lost. Once you execute him, he’s dead forever. I am less certain of the 100% certainty now than I used to be.
I knew a guy years ago when we were in the Army. He got out (less than favorably) and a few years later he and another guy killed three people in a bank robbery. They got less than $2500. The guy pleaded guilty and dared the judge to sentence him to death. The judge did, and the guy played tough for about 12 years, until his death warrant actually got signed. Then he raised all kinds of havoc with the system, and finally agreed to plead guilty in exchange for not receiving the death penalty. He should have been executed years ago but still draws breath.
In the event of wrongful execution, the damages can be paid to the estate.