Before we get into this I'll define those two straight up:

Sadism:
The deriving of pleasure, or the tendency to derive pleasure, from cruelty.

Justice:
The quality of being just; conformity to the principles of righteousness and rectitude in all things; strict performance of moral obligations; practical conformity to human or divine law; integrity in the dealings of men with each other; rectitude; equity; uprightness.


Now then.
The question becomes, is the Death Sentence based around sadism or justice?
Reasons for sadism:
People are killed slowly(there is no instant death), and sometimes painfully(Gas chamber).
Reasons for justice:
???

And so on and so forth...have fun.