Case life is definitely the biggest advantage, and it doesn't matter when you anneal if that's all you're after.
From what I've seen annealing also increase consistency in sizing and velocity. It seems to be cumulative over several firings, so annealing at any point will improve consistency.
Brass work hardens both when it's sized and when it's fired. It's easily measurable if you have the right tool, I just don't have the tool so I couldn't measure when I did my testing.
For consistency, you want every piece of brass in the same state when it's sized. If it's not you'll get different amounts of springback. Annealing "resets" brass that has been work hardened by firing to a consistent state. Nothing that happens between sizings is reliant on the brass being in an identical state of hardness, so there's no reason to anneal after sizing.
Sizing should also be a more consistent process than firing, so it should work harder brass by a more consistent amount. I have no data to back this up and I don't believe it would be measurable.
Much of this is more theoretical than practical. Odds are as long as you're annealing every cycle you're not going to let your brass harden enough to see a measurable difference in any metric. There's no theoretical or practical reason to size before annealing, which is why AMP and other annealer manufacturers say annealing should always be done before sizing.
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