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Full disclosure on my time with Battle for Azeroth thus far: I leveled a Horde character to 120 and completed all three Zandalar storylines plus put about 20 hours into end-game content. I have also leveled an Alliance character partway through Kul Tiras and completed portions of the Stormsong Valley and Tiragarde Sound storylines. My only experience in Drustavar has been through the eyes of the Horde thus far.
Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide