Bible translators for any given version of the Bible (e.g., NIV, NASB, NKJV, RSV, NRSV, and so on) differ on how to translate a given word. Rather than being a reason for perplexity, these differences can potentially become a reason for gratitude. Why? Because they often give us a depth of meaning we could not otherwise appreciate.
You're wondering which of the following is to be the preferred translation:
In the CONTEXT of Genesis 32:28, all three translations are quite accurate and meaningful.
Genesis 32 is a pivotal chapter in Jacob's life, and by extension it can become a pivotal chapter in the lives of the readers of the chapter. Here are some factors to keep in mind in making sense of the "big picture."
Jacob left Canaan with his tail between his legs. Because he thought he could obtain God's blessings through trickery, skullduggery, and deceit (what today we would label "fleshly" means), he left in fear. HOWEVER, he left with a promise of God--and interestingly, but not coincidentally, that promise was given in the presence of angels (cf. 28:12 and 32:1).
Jacob returned to Canaan a changed man. Twenty years have passed, and Jacob had done well, materially speaking, during that time. He is now beginning to realize--and his wrestling experience simply confirms this--that he had obtained the blessing of God not through trickery, skullduggery, and deceit, but simply through the promises of God. Notice the similarity between 28:13-14 and 32:12. In the former passage God promised His blessing to Jacob because it was His intent and His choice and plan all along.
In the latter passage, this truth finally dawns on Jacob. He's beginning to see that human effort alone is not sufficient to acquire God's blessing. Quite the contrary. God's blessing is contingent on His promises, and His promises alone. At last this truth dawns on Jacob as he turns to God in prayer (vv.9-12). As Jacob left Canaan he bargained with God in tit-for-tat fashion and made a vow that if God would bless him, provide for him, protect him, and prosper him,
"'then the LORD will be my God'" (28:21).
In exchange for God's blessing, Jacob would give God a tenth (big whoop!).
As Jacob returned to Canaan, however, his attitude toward God has improved, and he is beginning to see that he is indeed
"'unworthy of all the lovingkindness and of all the faithfulness'" which God had shown to him (v.10).
On the basis of God's promises, Jacob then asks the LORD for deliverance from his brother Esau, whom he had defrauded, and he prepares to re-enter Canaan. Before he does, however, God has a little object lesson for Jacob, and here is where the three differently translated words (above) come into play.
The LORD and Jacob Wrassle, and Jacob Prevails?
God obviously wanted Jacob to remember and even memorialize his first true act of repentance--his breakthrough with God--by engaging him in a "wrasslin' match." God allows him to "prevail," which we should note is not the same thing as Jacob prevailing. In my anachronistic way of thinking, God let Jacob prevail (well, at least to the point of a "draw") to teach him an important lesson; namely, Jacob's true battle in life is not with men, but with God. God wanted Jacob to strive, but only in God's way, which is by claiming boldly God's promises to him in spite of his unworthiness.
A Rose Is a Rose, By Any Other Name
In conclusion, whether we translate the Hebrew word in question as men, humans, or mortals, the meaning in the text and the meaning to Jacob is essentially the same:
You, Jacob, are just a man, and I AM the LORD God. I am transcendent, and you are but a man to whom I have made promises. You need to know your place in the grand scheme of things.
You, Jacob, are just a human being, created in my image. That image, however, is spoiled by both nature and nurture, and you therefore need to recognize your unworthiness in receiving the least of my blessings.
You, Jacob, are mortal. My promises to you will survive your passing and will extend my blessing to all the nations of the world, at no thanks to you. My promises and covenants can never fail, since I AM the LORD, and the sooner you realize my Word will come to fruition in ways you can never appreciate fully as long as you live, the better. I, on the other hand, since I live forever, will bring my covenant with you to completion in my own time and in my own way.
You, Jacob, I do not need; rather, you need me, and as a reminder of this truth I'm merely going to "touch" you, and thereafter from that merest of touches you'll walk with a limp, carrying the memory of your confrontation with me for the rest of your days. Moreover, I'm going to change your name. You were a conniving supplanter, but you are now a successful striver with Me. You are beginning to see that man does not experience my blessing by contriving but by striving according to My purposes and plans, which come to fruition as you demonstrate great humility and faith.