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Which of the titular phrases is the most appropriate and correct to express a work or task that mainly relies on the intelligence of an entity?

Stats of matches from Google Books: Intelligent-intensive (762) ; Intelligence-intensive (1840)

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    Most of the occurrences of 'intelligent intensive' that I've found in a Google search seem to be for a larger string like 'intelligent intensive care' where 'intensive' is part of a compound noun.
    – Edwin Ashworth
    Commented Mar 31, 2018 at 19:30

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"Intelligence-intensive" is correct.

Here "intensive" implies that a relatively large amount of something (by something I mean an abstract noun) must go into creating the product, whatever it is. "Intelligent" is an adjective, whereas "intelligence" is an abstract noun. The phrase itself ("[noun +]-intensive") is a modifier that describes the difficulty of making the product. It's actually an example of a compound modifier. Compound modifiers only consist of two adjectives in special cases where the two adjectives together describe some intermediate state that could not be expressed with just one of them. In other words, neither adjective can be used alone. For example, "bottom-right corner" or "grayish-green skin."

Compare your phrases to examples you know are grammatically correct, like "time-intensive" or labor-intensive," and you can see "intensive" is always partnered with an abstract noun. You probably instinctively have a sense that saying "laborious-intensive" instead of "labor-intensive" would not be right.

I'm sure there are examples where concrete nouns could be used as well, but the point is a noun must be used, not an adjective.

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It seems that "intelligence-intensive" is by far more prevalent. You can use this Google Ngram Viewer - https://books.google.com/ngrams

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