What a great question! This should net some really insightful answers. Hopefully no one minds, but I thought I would share my thoughts about both sides. This is my take after four-ish months of exposure to this stuff:

Where and how do you feel the opposing position (GC or QT) has been most or least convincing?

QT is least convincing to me primarily because it doesn't rely on facts to make assertions or arguments. Instead of presenting facts, it seems like the strategy is mostly to try to discredit anyone else's facts or make one question them. I see arguments made in its name as 'anti fact'. The most convincing part of their arguments, though, is the encouragement for people to look at terms and words as being entirely changeable--nothing is static, anything can be anything, which is idealistically very attractive (it's what I like most about that perspective).

GC is fact-based, which appeases my rational side as everything they share and assert makes sense. QT people can be guilty of this too, but I don't like seeing when GC people get into name-calling and nastier insults, and that's probably what I see as hurting GC the most (but that's just my feeling about it, idk if that's really impactful or not). Both sides have bullies and people who can be a little mean to others, but since GC has strength in the ideology and beliefs, then I feel like this is what hurts GC the most.

Do you feel their style of argumentation is effective?

The QT style of argumentation is very ineffective and off-putting to me; it comes across as so authoritarian and cult-like, like 'it's this way because I say so'. That makes the arguments very weak to me, because everything is presented as though it is impossible to challenge it. Nothing about the argument really feels dynamic.

The GC style of argumentation is much more effective because it's fact-based and adaptive because of that. It's direct and with supporting evidence, so I don't know that I've really seen any GC people stumble when arguing in its favor. To me, the directness can be intimidating because of the confidence and assuredness, but that's also valuable too.

How about the integrity of the argument itself?

On the very surface, the QT argument seems really wholesome and well-intended, but it falters at any level of questioning, I feel. Part of what seems difficult for that perspective is that they are defending an ideal that is being asserted as fact but focusing only on really using subjective facts (like stating 'I am a woman because I say I am'). The argument feels really, really weak, in my opinion.

GC's arguments are supported and upheld with facts of all kinds used in all different scenarios. It's adaptive, which to me is the greatest indicator of its integrity as beliefs that stand up against almost anything.

The express or inferred intentions of the author or speaker?

I think most of the QT people I've seen (just like internet posters) have good and honest intentions. I think most really mean what they say, so I don't think they're hiding anything. But from experience, I am wary to take them at face value when they assert that they are inclusive of people like me since there've been countless times that as soon as I question something or mention something that might be construed as GC that those people who were trying to portray themselves as my friend and ally suddenly become hostile. This has happened often enough that I just don't trust QT posts or people claiming to be my friend or to care or any of that.

GC people tend to seem more blunt, which I appreciate. I'm not a blunt person at all, so I tend to really like that quality in others--I generally respect that kind of honesty and it's easier for me to trust people like that. The trade is (and this is why I have trouble with it myself) that it can be abrasive and feel hurtful, so sometimes I feel like the rather solid integrity of GC can be undermined by flippancy or self-righteousness of some followers, just because the facts maybe overshadow the human element sometimes. But, again, that's just how I see it from my perspective.

The consistency of position? The reliability of supporting data?

QT's consistency seems to rely on unquestioning obedience and repetition of its esoteric beliefs. Slogans like 'TWAW/TMAM' are the most consistent part of their beliefs, and there's really no way to argue any of it which is the only way to keep all of these beliefs consistent. I don't really see scientific data used in QT arguments very much, and it makes sense since QT seems to be more critical of science than accepting of it.

GC has the same conclusions no matter how they are reached. The beliefs are most exercised like thought experiments over and over in countless different ways and scenarios, so the conclusions and findings stand up to scrutiny. They're actively scrutinized by their own proponents. The scientific mentality behind GC gives me more confidence in the information that is presented in its favor than that of QT.