On the other hand, if you want to make as objective a case as you can to quality according to agreed upon standards of evaluation, I think that TWoK > Nu Trek can be made a fairly strong case.
No, because there's no such thing as an "objective case" regarding art and you can't agree upon standards except with like-minded people. You can convince
yourself that you're making a "fairly strong case," and that's all.
Matters are not as desperate as you suggest.
Disagreement about
any issue, requires certain agreements about other issues. We have to see, to some extent, the world the same way, to even disagree in the first place - otherwise people would not even understand one another.
The fact that we have voluntarily arrived at the same thread on the same BBoard out of all of the wide world of the internet is a sign that we have some things in common already.
If we were to slow down and earnestly discuss what we like about movies in general, what we like a about Trek, and so on. We would find plenty of common ground.
Now in such a discussion we would have to be careful to parse reasons why subjectively prefer one film over the other, as opposed to our objective standards on interpreting and evaluating it.
You've heard the phrase "guilty pleasure" before, right? It is an expression which involves an admission that our subjective preferences and objective standards do not agree. Moreover, it involves an admission that we can objectively devalue/select against a film we subjectively prefer.
After mapping out our common ground we could explore the case for either side. The more direct route is to make a case directly centered on appealing to an agreed upon evaluative standard. Indirectly (since evaluations turn on interpretations), we might argue for an interpretation of the film which sets it under a particular evaluation which allows us to make a objective distinction between the two.
Now here is the hard part. Such an exercise requires good will and intellectual honesty. It requires both parties to be willing to listen and to be willing to be persuaded. But it can be done.