I don't have any Linen to compare, but I had read about all sorts of different fabrics being used as strops, I had used a bag strap a few times, it was a fairly lightweight herringbone weave cotton/canvas which worked pretty well except for the fact that it was attached to a bag, next I tried a heavier strap that was designed to go around luggage this was not so good.
I did think that the benefit was slight compared to just not using fabric, ie just the leather, but now I am wondering whether the fabric may help to extend the life of the edge.
My experience tonight told.me that maybe it was worthwhile.
I made the R&D strop so that I could give fabrics a go quickly and easily, I can either cut the denim (it is lycra denim I think, though I didn't know that when I bought it) off and reuse the bars or just make a few more.
If you have a pile of off cuts maybe just give them a go. I am trying to think of a system where the fabric could be swapped out, something like two bits of wood with teeth on the insides that clamp together.
The strip I made is probably 28" x 3.25 inches, so when finished its about 26" overall.
The fabrics available from strop makers seem to range from nylon strapping to felt and linen.
As I say it seems to be good but early days yet.