Does an old strop work better than a new one?

I recently bought a new strop because I heard that linen improves a coticule edge, so I bought one with a linen side. My new one is also a little wider than my old one. But what I have noticed is that I can get a better edge and quicker if I finish with my old strop and I'm wondering why this is. Is it because older strops work better when they as worn in, or is it more to do with the type of leather, or is it something completely different such as - is my technique wrong now that I have a wider strop? To add to the confusion, my new one was more expensive, so is it true that more expensive does not necessarily = better?