You should equip new quest rewards when their item level starts beating out your previous set of gear. If you are currently wearing Tier 21 gear, it is best to let the quest rewards significantly beat your existing item level before using them. While a Tier bonus is worth a fair chunk of damage, the stats will quickly fall behind. Azerite gear additionally is another 1-3% per bonus, on top of raw stats.

Formerly, when you visited a new zone, you would be very careful, tiptoeing around, cause everything was higher level than you. But as you dinged (leveled up), you would get more powerful relative to the locals. So you would feel more confident and capable. Dinging came to represent more HP, more Mana, better hit ratio, more crits, more talent points. you felt REALLY good when you dinged, like you had accomplished something. Almost tangible. You would think "now I can go back and take that mob/group that ganked me". And then when you had done all the quests, you would move to another zone and do it again. Fun!