"Making music" and "music making" as a noun

Constructions with the gerund are sometimes noun-like and sometimes verb-like (and sometimes the distinction is blurred).

The first of each of your pairs is verb-like, whereas the second is noun-like. One indicator of this is that the dependent goes in front of the gerund in a noun-like construction but after it in a verb-like one - which obviously is the difference you've noticed.

In each case the main verb wants a noun phrase as its subject, so the second is preferable - but I'm sure you would find examples of the first.

In a formal context the first version of each would be turned into a proper noun phrase by saying something like the hunting of whales. For example, the (UK) Hunting Act 2004 provides the hunting of rabbits is exempt if....