I've tried 3 different ones now
1. The Moby wrap (or 'African earth mother' look) is comfy and very good if you're going to be walking for a while (eg. long IKEA trip/walk in the park). BUT, it's a bit of a pain if you have to keep putting the baby in and out. It seems very comfortable for my LO and keeps her close and warm, (too warm in some cases as the fabric is quite thick so I have to think about how I dress her). No problems falling and staying asleep in this one! There's also a high weight limit, 25kg, on it so it'll last for longer.
2. Baby Bjorn (or the 'proper carrier'). This is fantastic for carrying the baby around the house or for short trips out as it's so easy to get them in and out. It seems very comfy for LO and she regularly falls asleep in ours (so it's also good that it's easy to remove the baby without waking her). This is definitely my favourite and has got much more use from the both of us than the Moby wrap. Only downside is that it is only up to 11kg so at the rate that LO is growing it won't last long.
3. Baba sling. To be honest, I regret buying this one. I could never get comfortable wearing it and LO never looked too comfy either. I also didn't like how her chin always got tucked into her chest no matter how I put her in it. So, it hasn't really been used at all so far. However, I can imagine that it will be by far the most comfortable for carrying an older baby or child around in the 'sitting on the hip' position so hopefully it will justify the money I spent on it sometime in the future!
Hope this helps
PS - have to say that I never breastfed in any of them (I'm not that bothered about covering up) so I would always take the baby out and feed them normally. But from some of the wrapping styles I've seen I'd say that the Moby wrap is the one to go for breastfeeding .