I hardly ever play PvP so definitely take this with a grain of salt, but when we play with PC players (my friends and I are all on Xbox with one person on PC who plays with us sometimes) we don't really notice a problem and my friend who plays with us on his PC has never complained, but when we get matched with PS players it almost always feels laggy. I've heard basically everyone in my clan complain about crucible against PS but no one really complains about PC (initially yeah, but not for a long time.)
Not saying that's how it is, just that's been my experience.
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Stadia is way worse than PS - and I'm on Xbox.