Not really sure what stone mulch is, but that's neither here nor there.
Not to be "that guy," but we use non-woven geotex fabric. As much emphasis as possible should be placed on how little "stone mulch" we actually use...maybe a few ton a year, at best. We have lots of non-woven geotex for our jobs, so it's really a no brainer (and typically a no-cost option for us). If we allot 2-3 rolls of geotex for a project, and we have some left over, it doesn't get throw away. It's no issue for us to cut a few strips for decorative gravel, typically only over french drains for our projects.
That's about all I've got.