Quantifying flavor differences between varieties? Different coffee varieties can produce very different flavour profiles. 
A different flavour profile points to differences in the chemical mix inside the cup. 

Are there any studies that quantify these differences?
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These links, including the redesigned coffee lexicon might help answer your question

http://worldcoffeeresearch.org/images/pdfs/WCR_Sensory_Lexicon_Edition_1_2016.pdf

https://en.wikipedia.org/wiki/Furan-2-ylmethanethiol

EDIT:

Additional information on the chemistry of coffee taste. This is produced by what we know as the Maillard Reaction -  the Maillard Reaction (MRx). Discovered by a French chemist in 1910 the MRx is what is largely responsible for transforming the mere handful of compounds found in green coffee (unroasted) to the complex aromatic beverage that it is today. As temperatures reach 150°C (302°F) the MRx causes free proteins to combine with sugars to form aromatic compounds such as furans which impart sweet, caramel like notes to the coffee. :

More on this chemical reaction  here: https://www.coffeechemistry.com/library/coffee-science-publications/unlocking-coffee-s-chemical-composition-part-2

Remember. Coffee differs from region to region - water, soil, temperature, altitude, sunlight, humidity, etc. Many, many factors go into how coffee gets its distinct flavor and notes.