Screwing the channel to the joists (with or without the rubber you mentioned) is creating a coupled system.
Inserting the channel into the clip array is creating a decoupled system. Much more lossy connection.
In a coupled system, much will be defined by the contact points, their quantity and role in conduction. In a decoupled system, the contacts are less of an issue, and results are determined by the degree of free-flex created by the 25 gauge channel and the essentially non-fastened attachment to the clip.
Clips are not categorized by ceiling clip vs. wall clip. The two piece clips available from many outlets have an advantage in the low frequencies. The Neoprene in the 2-piece clips act to damp the excursion of the components, as well as damp some of the vibration coming from clip components. This is why a two-piece clip tests better than a one piece clip.
There's a lot going on