Are these really equivalent?

The distinction is a pretty complicated matter and depends also on the register you are using. Here is a page which explains it and also offers a little test in the end to check your understanding: https://www.francaisfacile.com/exercices/exercice-francais-2/exercice-francais-105504.php

-- Chris (not a native speaker)

I don't see them as interchangeably equivalent. They serve a similar purpose but in some instances you need one where you can't substitute the other. I believe the site to which I postet the link in my previous post explains it pretty well.

-- Chris (not a native speaker).

Hi everyone,

I don't think 'dont ' and 'duquel' are always interchangeable.

In the examples given in the lesson , the verbs all use de :

avoir envie de , avoir peur de, parler de, avoir besoin de ...

In thoses cases you can use any of the possibilities suggested .

Hope this helps!

It would be nice to be able to refer to a list of verbs that use prepositions. 

Hi Robin,

It is in my To-Do list....

Here's one!  Not exhaustive of course, but has a lot of verbs.

https://www.thoughtco.com/french-verbs-with-prepositions-p2-1364548