Well the # already looks a bit like a gate that's falling over, which is presumably what's scandalous about it.
I am personally more annoyed by -Gate, because it just sounds really dumb and useless. Hashtags, on the other hand, are used a lot more generally and widely. It's like a subject line in an email; it characterises briefly what the thing is about. #blacklivesmatter or #jesuischarlie at least tell you something about what's going on and serve to characterise the movement, as distinct from other movements. GamerGate or ModGate are just stupid.
Personally, I've always saw -Gate as a way of making fun of people who make mountains out of molehills. E.g. GamerGate was such a massive and ludicrous over-reaction to a rather mundane thing that nobody would ordinarily give two hoots about. Putting it on the same sort of level of scandal as Watergate just highlights the idiocy and childishness of the people who took that thing seriously. #hashtags can be used for similar comedic effect, but it seems to me that almost all -gates have an inherently ludicrous quality, while a large number of #hashtags are actually pretty serious and important. In any case, there's no historical context or precedent for #hashtags, whereas when you use -gate, you should be aware of what the original -gate scandal was.
#ActuallyIt'sAboutEthicsInVideoGameJournalism
