It is not an issue of translation but of selection. Given that the LXX version is very early, that it is witnessed in the DSS vorlage, and that it is reflected in the Targum Pseudo-Jonathan (Jonathan Ben Uzziel), I would suggest that the NWT chose wrong. This suggestion is supported by many of the world's leading scholars, including Emanuel Tov. Meanwhile, bible.org revers to the Masoretic variant in the following note ...
14 tc Heb the sons of Israel. The idea, perhaps, is that Israel was central to Yahwehs purposes and all other nations were arranged and distributed according to how they related to Israel. See Driver, Deuteronomy, 355-56. For the MT la@r`c=y] yn}B= (sons of Israel) a Qumran fragment has sons of God, while the LXX reads ajggevlwn qeou' (angelwn qeou, angels of God), presupposing la@ yn}B= or <yl!a@ yn}B=. Sons of God is undoubtedly the original reading; the MT and LXX have each interpreted it differently. MT assumes that the expression sons of God refers to Israel (cf. Hos. 1:10), while LXX has assumed that the phrase refers to the angelic heavenly assembly (Pss 29:1; 89:6; cf. as well Ps 82). The phrase is also attested in Ugaritic, where it refers to the high god Els divine assembly. According to the latter view, which is reflected in the translation, the Lord delegated jurisdiction over the nations to his angelic host (cf. Dan. 10:13-21), while reserving for himself Israel, over whom he rules directly. For a defense of the view taken here, see Michael S. Heiser, Deuteronomy 32:8 and the Sons of God, BSac 158 (2001):52-74.
I suspect that the NWT was either being sloppy or intentianally perpetrating an earlier harmonization. In either case, it does not speak well of the NWT.