I like both. If I could only pick one I would get a woven. I love a stretchy wrap those first couple of months when the baby seems so fragile. I love to pre tie a stretchy wrap before leaving the house and be able to just pop baby in when we get there.
I have a Wrapsody Bali Baby Stretch, which doesn't have as much stretch as a Boba/Sleepy Wrap or a Moby. I can still comfortably wear my 24lb 14 month old in it for short periods of time.
Wovens just last longer, look better and are light years more supportive to both mama and baby after the first couple of months.
Mama to Henry (01.07), Catherine (09.11), Audrey (04.14), Clare (09.15) and our newest addition, coming July 2017!