Is there a consistent way to transfer skill checks between various d20 type systems?
In D&D 5e, for example, a precedent is set for difficulty of skill checks, where 10 is easy, 15 medium and so on (or something like that, I don't have the books in front of me)
Surely it's possible to take scenarios that are inspiring from one game and place them in another, but this has the potential for the GM to make a lot of human error. I'm okay with taking a lot of time to transfer rules and playtest, but I'm wondering if there is an empirical way, a measurable and verifiable way, to transfer skill checks from any d20 system to another d20 based system. The verifyibility would be that players of an approximate power level have the same statistical capacity for success when moving from one system to another.
Is there a format or formula to follow? Have any materials been written on "porting" these skill checks and scenes?
The answer does not have to cover everything, but I am looking for something I can read that gives guidelines.
As an example, say that I made a scene I liked a lot for D&D, and wanted to port it to a new group playing in a different system more or less verbatim.
Players scale a tall seaside spire to a Roc's nest. Every 2 in-world minutes, a massive wave sends the imbalanced structure shuddering, and the players have to make a DC16 save to hold on for dear life. 150 feet up, the players are confronted with a harpy and must succeed a DC14 wisdom save (or something, I don't have the book) in order to not throw themselves off the cliff.
What are some materials or resources that I can call upon to "port" said encounter to another system? Are there any workable rules or formulas, or is it simply too broad of a question? I feel like there should be some relation to the possible success rate in games that share the same dice. I would think (perhaps incorrectly) that there is a correlation between the statistical probability of success and the number of sides on the die.