Stretchy versus non stretchy

OK, all, I've read a lot about wraps the last few days, and I've seen different people say things about stretchy wraps and I've seen other places recommend you get a fabric with stretch like knit or fleece. So, the wraps I made the other day were out of a ribbing, (read knit that you put around the top of a sweatshirt for people who are not sewing inclined.) so it was pretty stretchy. The other fabric I bought is a homespun 100% cotton. I don't have a baby yet to really try these with (I've been borrowing my friend's), but if anyone has an opinion on when and why stretchy or non stretchy would be better, please let me know. Thanks!