1st of all, have a look at this post from some days ago, it´ll help you with the distinction vs. FC & VC frameworks > https://www.preplounge.com/en/consulting-forum/when-should-i-break-down-costs-as-fixed-and-variable-as-opposed-to-over-the-value-chain-5990#first-answer.
This said, both breakdowns (FC & VC vs. Value Chain) can be perfectly fine if they are well argumented.
I would say that in most cases, Fixed vs. Variable is an easier way to tackle down these kind of problems. However, keep your eyes open for hints that point you towards a value-chain approach (e.g., issues in the process, total costs of revenues going down in time, etc.)
Hope it helps.