From the “Exodus” entry in the New Dictionary of Biblical Theology:
More directly than any other NT book, Hebrews argues for the superiority of the new epoch. In this new Exodus (3:7-19), Jesus, attested by signs and wonders and gifts of the Spirit (cf. Is. 63:11; Num. 11:25), is greater than both the angels who gave the first covenant (Heb. 2:1-4) and Moses who mediated it (3:2-6; cf. 8:5-6). We should therefore heed the warning example of the generation who through unbelief failed to enter the promised rest (3:12-19; cf. Jude 5).
Further, since Joshua did not provide new creational rest (Heb. 4:8), it still remains for us (4:1-11; Ps. 95:7-11). Bearing the sins of many (Heb. 9:28; Is. 53:11-12), Jesus, our new Moses and new Joshua, has gone ahead to provide perfect access to the Father (Heb. 12:2; 8:1; 10:19-20; 4:16) through his blood of the new covenant (13:20; 12:24; Exod. 24:8).
We, however, are exiles, still on the journey (Heb. 11:13-14; 13:14); it requires faithful endurance (11:39–12:3), and wilful disobedience will be punished (6:4-12; 10:26-31; Num. 15:30; 16:35; Deut. 17:12, 20). Our coming not to Sinai but Zion the heavenly Jerusalem means joy and not terror for us (Heb. 12:18-24; Deut. 9:19; Exod. 19:16-19). But if those who disobeyed the voice that shook the earth were punished, how much more those who disregard the heavenly voice that will shake both the heavens and the earth (12:25-29; Deut. 4:24)?
Nevertheless, we are comforted by the great shepherd of the sheep who came through death as Moses came through the Reed Sea (Heb. 13:20-21; Is. 63:11).
— Rikki E. Watts, “Exodus,” in New Dictionary of Biblical Theology, eds. T. D. Alexander, B. S. Rosner, D. A. Carson, and Graeme Goldsworthy (Downers Grove, IL: InterVarsity Press, 2000), 486.