' Greenbaum & Quirk say mention that in addition to the higher degree expressed by 'more', it also 'conveys a comment on the inadequacy what is said in the linguistic unit it modifies'. In your example, her intelligence is not merely more effective than her experience, but also the experience (or lack thereof) is not nearly so important in the situation.
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Here's another example:
The amount of rainfall more than doubles between May and June.