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For some thoughts on bleeding:
This is something I've fought about a fair bit when trying to make longswords less bad against good curing. My conclusion basically comes down to this: classes without either (1) dryblood to complement haemophilia or (2) excessively high bleeding values just are not good at bleeding against artefacted targets. This is because imperian bleed classes are very much attrition rather than burst, which means a single roll of the di on the nightshade eat can be a full progress reset, and because kill sequences tend to be fairly long, the reallistic chance of that lucky haemophilia cure happening is extremely high.
This is partially because of how bleeding works with being able to instantly clot it all away as well, but that's a far mor far reaching change and fairly necessary just because of teams. This is also why dk's position is so tenuous - teeth somewhat works because the values are too high, but if they weren't high they'd be in just as subpar a position as templar (and arguably they still have the same issues, it just comes down to how much artefact weight the target can throw at the problem). Its also why rg actually does its job fairly well (though rg suffers from many of the other issues). Naturally, runeflares obviously help.
I would personally recommend avoiding bleeding for berserker. The successful bleed class formula hasn't really been nailed down yet for the classes its already used by, adding another one into the mix is probably not going to work out. Impatience could work, though personally I feel one of the biggest issues berserker suffers is that outside of its endgame there's not much going on - there's no mid fight pressure etc. The target can basically go full throttle the whole fight until the execution phase where they just have to play safe for a few seconds. That execution phase is actually pretty good, its just in a vacuum so is trivial to deal with.
Its not a coincidence that most people play the classes that can kill outside of their closers if the target plays poorly. I think if this part of berserker can be improved it would see much more adoption.
To be honest I think the comparrison is irrelevant anyway. Assassin and shaman play very differently (assassin is arguably far more of an attrition aff class whereas shaman is a lot more bursty). It probably doesn't matter a huge amount as one being op (or not as the case may be) doesn't inherently mean the other is or isn't.
They're both incredibly strong classes. I don't think anyone is going to contest that fact.