Pragmatic difference between two structures like that vs like it that [duplicate]

Both are correct, and both convey the same information. The only difference is in the syntax: the grammatical way in which you are conveying your point. Let us look at the first example:

I like it that your lack of concern is my fault.

The word that has many uses in English. In this example, that is the relative pronoun, and refers back to it so as to give more information.

What do you like? You like it. However, the listener knows nothing about what it is, and so you add a relative clause, beginning with that, which gives more information about it. Similar constructions include the following:

This is the house that I want.

Here is the man that I was talking about.

The only good thing that happened last night was...

As for your second example:

I like that your lack of concern is my fault.

That is a type of subordinating conjunction, called a complimentizer. Unsurprisingly, it takes the second clause and makes it the complement of the first clause. Because of the complimentizer that, the whole phrase your lack of concern is my fault becomes the object of the verb like. Similar constructions are as follow:

I said that I wanted to.

He hopes that his brother will come home to see him.

The king commands that his fool attend the court.

As you can see, both constructions occur frequently in English and neither is inherently better than the other. If I am to make a recommendation, however, the it in the first example feels superfluous; it doesn't contain anything necessary in and of itself. As always with style, the choice is ultimately yours.

In spoken English, there really is no difference between the two. They are equally acceptable. I rarely hear the "I like it that" form, as people tend to eliminate any unnecessary sounds and words when speaking.

If you're being sarcastic (which you certainly are with a sentence constructed the way yours is), then I would omit "it". In fact, I can't think of a good reason ever to include it. It sounds a little stuffy.