Exodus 21 suggests that those who kill another man shall be put to death, whereas in the case of killing a servant they shall only be punished. Do you think that God viewed the killing of a servant or maid less serious?
The answer to your question is no, the Lord does not view the lives of servants differently than that of a free man. In Exodus 21, the Lord demands the death penalty for premeditated murder in either case. For free men, the Lord stipulated:
Ex. 21:12 “He who strikes a man so that he dies shall surely be put to death.
Similarly, killing a servant with malice results in the death penalty:
Ex. 21:20 “If a man strikes his male or female slave with a rod and he dies at his hand, he shall be punished.
Ex. 21:21 “If, however, he survives a day or two, no vengeance shall be taken; for he is his property.
In Hebrew, the same word (naqam) is used twice in the passage concerning servants. In v.20 it’s translated as “punished” while in v.21 it is translated “vengeance.” So given the context of Exodus 21, vengeance and punishment are both references to the death penalty. The Law says that if a master strikes a slave with intent to kill (premeditated murder), then the master will receive vengeance, which is a reference to a life for a life as described elsewhere in the chapter.
On the other hand, if the slave lived a day or two and then died, the master’s actions against his slave were considered an unintentional killing (i.e., manslaughter), which was not punishable by death. Instead, the master’s consequence would be the loss of property, because his slave's death cost the master financial loss.