Interesting question...
Leaving aside magic items which replicate a particular light-generating spell (where it should be clear by its level how it interacts with Darnkess), I don't think there is a written rule, so the obvious answer is "the DM decides what happens".
Perhaps I would differentiate between magic items the main the purpose of which is to illuminate or generally improve vision and detection (making them beat Darkness) such as a Lantern of Revealing, and magic items where their light-shedding is a minor or secondary effect (making Darkness beat them) such as a Flame Tongue. In the latter case, Darkness would only suppress the light effect of the magic items, not its other properties, i.e. the flaming sword would still deal fire damage even if you can't see the fire.