In terms of support for you and her, the Moby beats the BB hands down. It offers a much wider seat, and holds her close to you so she's not just hanging from your front.
But you do need to wear the Moby tighter than you might think. She shouldn't be scrunched up in it really.
When you say she doesn't like the "frog like position" in the Moby, have you got her legs tucked inside the sling, or hanging out?
The froggy position, with her knees higher than her bum is the best position for her developmentally, and is a very natural position for her to be in. That said, not all babies like having their legs tucked inside the sling. So if they are inside and she's sort of sitting on them, it might be worth trying her with legs out.
If you're really not getting on with the wrap, then something like a Manduca will be a better option. This can be used from Newborn, and I can still carry my 17 month old in one. Although we use woven wraps really.
Again it offers a nice wide seat, which the BB does not. And offers the option of back carries once she's older.
Hope that helps x