What is the difference between both of them? I could not find any explanations so I came here.
The reason you could not find any explanation specifically about them is because the difference can be explained as a generic difference between a te-form and a masu-stem:
- なく vs. なくて and stem form vs. てform as conjunctions
- Connecting phrases with the stem of masu-form
- Stem of ます-form as conjuction
- て versus combining-form for joining clauses
- Is there a term for using conjugating verbs such that the sentence continues with another clause?
Since もとづく is already a stiff verb, the difference between もとづいて and もとづき is small, and they are interchangeable. Still, もとづき sounds relatively a little stiffer or more academic.