"Of" in this case appears in its occasional role as a regular preposition (although it is a bit special in that it can only modify nouns, not verbs). The verb-subject ordering in your example sentences makes it a little more difficult to see, so I'm going to reorder the terms to demonstrate the links:
Our increased use of technology is of crucial importance to our progress.
The sentence above and both of your examples all have the same meaning. That is, the same facts are made clear to the listener in any of these cases.
The emphasis, as you rightly suspect, is slightly different in each case:
It is of crucial importance that we make more use of technology if we are to make progress.
- Using the noun form of "importance" elevates the urgency of the assessment even higher, as does the more formal construction (consider an alternative: "It's crucial that we use more technology..."). This calls greater attention to the immediacy of the situation.
It is crucially important that we make more use of technology if we are to make progress.
- Here, "important" is an adjective, so, while there's still a fair amount of immediacy given by the emphatic redundancy of "crucial" and "important", the specific method being recommended is emphasized a little more.
Basically, this "of" is a noun-modifying preposition that lends formality and re-emphasizes "importance".
At some point, they're close enough that the choice is more of a feeling than anything else. I happen to agree with @Daniel that the former construction is more pleasant, but my only guess as to why that might be is that the latter uses an adjective/adjective stack, that, beyond seeming more redundant than the adjective/noun in the first example, seems to imbalance the sentence a bit as the listener awaits the eventual noun on which to place these terms.
You may find this tool useful in the future (though it is not particularly user-friendly).