"Paul and Barnabas met this false doctrine with promptness and opposed the introduction of the subject to the Gentiles. On the other hand, many of the believing Jews of Antioch favored the position of the brethren recently come from Judea. AA 189.1"
"When therefore Paul and Barnabas had no small dissension and disputation with them, they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question."
Both passages describe the disagreement between Paul and Barnabas and certain Jewish believers regarding doctrine (circumcision of Gentiles). Acts 15:2 describes the dissension and the decision to go to Jerusalem, while the EGW passage describes the initial conflict in Antioch. The thematic parallel is clear and direct.
"The Jewish converts generally were not inclined to move as rapidly as the providence of God opened the way. From the result of the apostles’ labors among the Gentiles it was evident that the converts among the latter people would far exceed the Jewish converts in number. The Jews feared that if the restrictions and ceremonies of their law were not made obligatory upon the Gentiles as a condition of church fellowship, the national peculiarities of the Jews, which had hitherto kept them distinct from all other people, would finally disappear from among those who received the gospel message. AA 189.2"
"But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses."
The EGW passage describes the tension between Jewish and Gentile converts regarding the observance of Jewish laws and customs. Acts 15:5 directly addresses this issue, with believing Pharisees insisting on the necessity of circumcising Gentile converts and requiring them to keep the law of Moses. The EGW passage provides context and expands on the underlying concerns of the Jewish converts.
"The Jews had always prided themselves upon their divinely appointed services, and many of those who had been converted to the faith of Christ still felt that since God had once clearly outlined the Hebrew manner of worship, it was improbable that He would ever authorize a change in any of its specifications. They insisted that the Jewish laws and ceremonies should be incorporated into the rites of the Christian religion. They were slow to discern that all the sacrificial offerings had but prefigured the death of the Son of God, in which type met antitype, and after which the rites and ceremonies of the Mosaic dispensation were no longer binding. AA 189.3"
"For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect."
Both passages discuss the idea that the Old Testament sacrificial system was a shadow or prefigurement of Christ's sacrifice, and that with the fulfillment of that sacrifice, the old system is no longer binding. EGW explains the resistance to this idea among Jewish converts, while Hebrews 10:1 explains the ineffectiveness of the old sacrifices.