Is there way to compare computing power used in two blockchains when every one of them is using different mathematical function as a Proof-of-Work? If I am a Bitcoin node, I can evaluate two blockchains in terms of each one consisting of more Terahashes than the other and thus deduct which one is the "correct" one. There is impartial source of consensus - hashes done. But what if I had two blockchains, each one making a different function, e.g. one is Bitcoin and making SHA-256 and another is making other random computation. Could I impartially deduct which "chain" has the most computation power spent even if in those two chains the "way" this computation power is spent is different? Is there common impartial denominator then?
Or, to make it even more interesting, if a blockchain had self-amending possibility like Tezos, and in a certain point of time it reached a consensus to change it's Proof-of-Work method to e.g. more memory-hard (in order to discontinue usic ASICs) then could a node that wasn't connected to the network before that change somehow use a common denominator of computing power (now not necessarily Hashes used) to evaluate the right chain by checking how much computing power was spent on chain both before the amendment (when e.g. SHA-256 was used) and after change (when some new Proof-of-Work is used)?
Short answer - no. Any denominator used to compare computing power spent on two different functions would be subjective to those functions. Therefore it cannot be source of consensus spreading over many functions. It'd like comparing apples to oranges.