i think you need to look more carefully at the differences at the various components and why some are preferred for particular tasks. to me it seems that you're going based on a 'hype' of some sort.
as i already said, linen is a bit more abrasive than cotton, but that makes it 'better' only if you want more abrasive fabric side.
likewise latigo usually has more draw than a horsehide, and I believe that translates in more abrasion too, and that is better only if that's what you want (i personally am not a fan of it and prefer to use fabric and shell, but some people would rather use latigo only).
I have used the webbed fabric for few weeks and it seems to work very well. I hear it is very good for pasting as well, but I also hear that the wool is the best surface if you'd be using diamond paste as it doesn't produce the typical harshness on the edge that diamond does.
so, you should answer the following questions
- what do I want from a strop that my current strop doesn't provide
- what will horsehide give me instead of, or in addition to the latigo I have
- what will a second latigo give me
- what will a second cotton, or a linen, wool, or webbed fabric give me
unless you know why exactly you are getting it, you are buying another strop just because you can afford it and in this case it makes very little difference what you get, and would make sense to get something that you don't currently have, both as leather and as fabric.