All cables are critically important and any particular type of cable can be as transformative and critical as any other. I have demonstrated that continually in hundreds of systems.
Zovato, your question is motived by sincere desire to discover, I believe. But as with the bulk of the audiophile community, these kind of questions are not productive because audiophiles fail to assess and use cables correctly.
I discuss in my book, The Audiophile Laws, that the only way to properly use and assess cables is in complete sets. There is no way to knowingly advance a system by ad hoc combinations of cables, much less gain any insight as to which type of cable might be the most influential. When the audiophile works with complete sets of cables and adds them incrementally, it becomes obvious that there is no one type of cable which is most important or has the most influence on a system.
One of the errors of system building is the belief that certain cables influence the system more than others. Consequently, some audiophiles will spend on speaker cables and not much, if anything, on power cords. As such, attempts to peg a particular type of cable result in dumbing down the system if it leads to emphasizing one type over another.
The different geometries and conductor material of cables when compared assures that results across the community will be disparate. There is no consensus and no forward movement in system building by surveying which type of cables the community thinks are most important.
There is only one proper way to work with cables, in complete sets. After the gross comparisons are done and the "winner" is selected, then, perhaps swap out a single cable to tune the rig.