The change from Matthew 7:1-2 comes in verse 1. The final phrase, “Judge not, that ye be not judged,” is the same as in Matthew, where it is the whole of the first verse.
The rest of verse 1 has Jesus turning from addressing the twelve, as described in 3 Nephi 13:25, and now addressing the whole congregation. The distinction that the ending verses of Matthew 6 and 3 Nephi 13 is principally in having those verses being given to the twelve rather than as commandments to the whole congregation.
Verses 1 and 2 set up a complementarity of action, where the way we behave towards others on earth will be a model for how God will behave towards us at the time of judgment. The point is certainly not that we should not judge. The very nature of agency requires that we make constant judgments. The admonition does stop with “judge not.” It continues to tell us what the caution is.
Verse 2 continues to explain the complementary nature of our judge. Whatever measure we use to judge our fellow human beings, that measure will be used to judge us. Thus, if we are unforgiving of small errors, God will similarly be harsh with our small errors. See the comments on 3 Nephi 12:7 for how this teaching correlates to Alma’s teaching of the doctrine of restoration.
Doctrine and Covenants 88:22–24 teaches us the principle that what we learn to become on earth will be an important aspect of our judgment:
22 For he who is not able to abide the law of a celestial kingdom cannot abide a celestial glory.
23 And he who cannot abide the law of a terrestrial kingdom cannot abide a terrestrial glory.
24 And he who cannot abide the law of a telestial kingdom cannot abide a telestial glory; therefore he is not meet for a kingdom of glory. Therefore he must abide a kingdom which is not a kingdom of glory.