Both deal with sin. In the case of Genesis 3:16 the sorrows of childbearing reminds mothers that they have inherited original sin and Genesis deals with doing penance for your sins. I also got from it, that we are to have dominion over our sins. Here is Genesis 3:16, and 4:7 from the Haydock Bible Commentary.
Ver. 16. And thy conceptions. Septuagint:“thy groaning.” The multifarious sorrows of childbearing, must remind all mothers (the blessed Virgin alone excepted) of what they have incurred by original sin. If that had not taken place, they would have conceived with out concupiscence, and brought forth without sorrow. (St. Augustine, City of God xiv. 26.)— Conceptions are multiplied on account of the many untimely deaths, in our fallen state. Power, which will sometimes be exercised with rigor. (Haydock) — Moses here shews the original and natural subjection of wives to their husbands, in opposition to the Egyptians, who, to honour Isis, gave women the superiority by the marriage contract. (Diod. i. 2.) (Calmet)
Ver. 7. Over it. This is a clear proof of free-will. To destroy its force, Protestants translate over him, as if Cain should still retain his privilege of the first-born, notwithstanding all his wickedness, and should rule over Abel, who would willingly submit, “unto thee his desire,” &c. But God had made no mention of Abel. The whole discourse is about doing well or ill; and Cain is encouraged to avoid the stings of conscience, by altering his conduct, as it was in his power, how strongly soever his passions might solicit him to evil. (Haydock) — The Hebrew is understood by Onkelos, and the Targum of Jerusalem, in the sense of the Vulgate. The latter reads, “If thou correct thy proceedings in this life, thou wilt receive pardon in the next world. But if thou do not penance for thy sin, it shall remain till the day of the great judgment, and it shall stay, lying at the door of thy heart. But I have given thee power to govern thy concupiscence: thou shalt sway it, either to embrace good or evil.” Calmet shews that the Hebrew perfectly admits of this sense. St. Augustine will not allow of the turn which the Manichees gave it. "Thou shalt have dominion over (illius.) What? thy brother! (absit) by no means: over what then, but sin? (City of God xv. 7.) Protestants formerly abandoned the translation of 1579, (which they have again resumed) and translated better, “unto thee shall be the desire thereof, and thou shalt rule over it,” which R. Abenezra explains also of sin. To which of these editions, all given by royal authority, will Protestants adhere? Luther wrote a book against free-will, and Calvin would not admit the very name. But we, with all antiquity, must cry out with St. Jerome, contra Jov. 2: “God made us with free-will, neither are we drawn by necessity to virtue or vice; else where there is necessity, there is neither damnation nor reward.” (Worthington; Haydock)
