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If two are activated simultaneously [eg, both trying to grab same item], the inserter that was placed first always gets priority.
This is due to the game cycling through a long list of all the entities in game each tick, as new entities are placed ingame they get added to that list, & dealt with in the same order.
Edit ~ source link: https://wiki.factorio.com/index.php?title=Inserters#Mechanics
Output inserters from an assembly machine take turns, if possible. You can build a test rig with 3 output boxes ~ all three should fill evenly.
That’s what I said. (Or wanted to say)
But that's way off topic, so back to what OP asked for, here's what I have found (please, do correct me if I'm wrong):
Depending on what the inserters are attached to, they will either try to fill evenly, or go by order of when they were placed. The latter system is very deep in the Factorio code and can be seen in several places, most notably in logistic networks with how storage chests work, where the bots will always fill the storage chests within the network based on when they were placed, rather than distance to the chest. It's one of many UPS/FPS saving tricks they have implemented into the game.
This mechanic, when it comes to inserters, is only observed when picking up from the same tile though. Since an assembler is 3x3 tiles and the "access tile" is any of the 9 tiles, inserters trying to take from an assembly machine will act differently (even if both are attached to the same tile, eg. two long handed attached to the center or two regular attached to the same corner). In cases like these, they will take turns to get items out of the assembly machine.
I have not done any tests recently for mixed types of inserters, so I don't know what will happen if you put a fast inserter, a stack inserter and a regular inserter to take items from the same machine.
This is good enough to me. Any more detail is not needed. If I need some other control over my inserters (say I want to prioritize item A over item B) I use wire.