Textual: The similarity here is that the term persecution is directly applied in both cases. The difference is that in the Saul text, it is the Lord who is persecuted. Here it is the church that is persecuted. The fact of persecution exists in both cases, but in the New World, the persecution is prior to the coming of Jesus Christ in the flesh.
Thus in one sense, there was no direct person with which the church might be identified and against whom one might persecute as did Saul in the Old World. Even though the New World church emphasized the coming atoning Messiah, that person was still understood to be Jehovah, and it is possible that Alma’s version of apostasy was similar to that of Noah and his priests, where he accepted much of the competing religion, but continued to hold to some of the Mosaic law.
If this were the case with Alma the Younger and the sons of Mosiah, they could not have understood a declaration similar to that given to Saul because they would not have believed that they were persecuting Jehovah, only those who believed in the future atoning Messiah. The difference in the message was essential to have them understand the import of their actions; that the church was equated with Jehovah, and should not be persecuted.