Hi there,
That's a great question. MongoDB, being a NoSQL database, allows data to be stored in arrays instead of being normalized as in a relational database like MySQL. This would help in storing the multi-level category structure that Magento maintains.
While Magento maintains different category levels by using a "path" variable, MongoDB would be able to store each product's category structure in a single column (as an array). This would make it easier for analysis.
In terms of performance improvements, this depends on the specific use case MongoDB would be used for. Could you elaborate on the end goal of your analysis?
Thanks,
Akash Agrawal, Analyst - Magento Analytics (http://www.rjmetrics.com)