Luna. It adds more damage, has a good proc rate and is easy to obtain for each character.
Sol doesn't heal you that much unless you're overleveled and relying on skill% to keep you alive on Enemy Phase is bad. Vengeance needs Vantage to be great. Astra is terrible against high defense enemies. Lethality has basically non-existent proc rate and you could already be killing enemies even if you could raise the proc rate to its highest.
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Sol sucks. It's an alright proc if its the only thing you've got, but: 1. In game its proc rate is not good enough to keep you up. 2. Post game you either kill everything anyways or Sol is doing nothing. No middle ground. 3. Sol interferes with other procs and makes you worse.
Luna's the most common and useful. Ignis is a rare, inferior, Luna. It's not worth using on anyone besides MU and maybe Morgan.
Astra is about as good as Luna during a proc. It's better than RFK for Inigo, but that's about it.
Vengeance if you've got Vantage access, and/or can reasonably control incoming damage.
Aether is the strongest non-Lethality proc, but it's rare, and doesn't have the best proc rate in the world. If you have it, though, and realize it's not a standalone, but instead a Synergy skill [use it with Luna!] it's amazing. But it's rare.
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cool. i'm glad luna is the best because i already have it on most of the people i use. i also never considered combining aether with luna before. if i do that, i should also put rightful king on as well, right?
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