The reason for the difference in scores has to do with how the two tools store data.
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Product Discovery offers cached data that is refreshed within a 30-Day period of time. This cached data is currently necessary in order to provide quick and accurate results from Product Discovery. Providing the quantity of data available in Product Discovery takes an incredible amount of computing power; a quantity that works best with a cached system in order to provide a great customer experience while still providing accurate data.

Market Intelligence offers data that tracks historical BSR and real-time BSR (among other statistics such as review count or estimated monthly sales) - statistics that are not based on a cached system, but rather very frequent updates.

What that means is that the product idea score you get from Market intelligence is most likely more relevant to the product. Ultimately the product idea score is not intended to be the last metric to take into consideration when you are validating a product idea. We recommend you use the score as a starting point. If you find a 5 star product that means it is worth the time to research it further. We also suggest monitoring the product idea score over time to account for fluctuations over time.