One argument is that "which" or "that" doesn't matter, as they have become interchangeable in very common usage, and since language evolves, well, that's that. (But not which's which. Ha.)
I prefer the rule (possibly more of a guideline) that says that "which" precedes an incidental comment about the subject (that is, it's not important to understanding the sense of the sentence), while "that" precedes something that is crucial to understanding the sense of the sentence.
For example, someone compliments you on your hat. You can respond: "This hat, which I love dearly, came from Afghanistan." The meaning of the sentence "This hat came from Afghanistan" is changed in no way at all by the "which" clause. It doesn't restrict the subject--"this hat"--because there is only one hat on your head and you can say anything you want about it but there's still just one hat on your head.
Compare to someone complimenting you on your collection of hats, none of which you are wearing at the moment. You can respond, "The hat that came from Afghanistan is my favorite." The sentence "The hat is my favorite" does NOT make sense without the "that" clause, because no one will know which hat you are discussing. It restricts the discussion to a specific hat out of many.
If you want the official terms, you use "that" for a restrictive clause--it restricts the discussion to the specific thing described (from the pile of hats, we're restricting the discussion to the one from Afghanistan), and you use "which" for a nonrestrictive clause--it doesn't restrict the original subject of the sentence in any way (the hat on my head is my favorite; the fact that it is your favorite doesn't narrow it down or restrict the discussion in any way.)
"Which" and "that" are complicated because they are used in a variety of ways that depend on context. (Hmm, you say, why did she use "that depend..." in this sentence rather than ", which depend..."? Yes, it gets subtle. My primary point is that the usage depends on context; I don't want someone to discard that clause as irrelevant. If I wanted merely to emphasize that they are used in a variety of ways and merely point out in passing that context matters, I could have said, "...in a variety of ways, which depend on context.") Yes. Here, the difference is indeed subtle; you have to decide what it is that you're really trying to say and see whether removing the clause changes the essential meaning.
Which house did Jack build? -- "This is the house that Jack built."
Is this the house where we're meeting? "Yes, this is the house, which Jack built." (The fact that Jack built the house has nothing to do with where the meeting will take place; it's just an interesting side note.)
The original question was posted as a comment to this post:
(1) This is a unique post THAT is an unusually useful one?
(2) This is a unique post, WHICH is an unusually useful one?
First, note the use of the comma with "which" as a nonrestrictive clause.
Next, to know which is correct, you have to figure out the writer's primary meaning. In fact, in this case, it's hard to tell. If you removed "an unusually useful one" from the sentence, leaving "This is a unique post," is the main meaning still intact?
I'd interpret the writer's underlying possible meanings as:
(1) This post is both unique and unusually useful. [Perhaps compared to other unique posts, many of which might not be useful, or useful but not unusually so.]
(2) This post is unique. By the way, it's also useful. [I admire the fact that it's unique. But I ought to mention in passing that I also found it useful.]