BBBs are our first choice for outings with DS (2yo) because of their super absorbancy, and DS is doing BIG wees now. No other nappy even comes close. I can easily leave these nappies on him for a good 3-4 hours. Most others need changing after 2 hours. I ALWAYS use a microfleece liner for dryness, but also because poo rolls off it so easily.
Having said that, I don't really intend using them much for NB as I think they would be hugely bulky. DS's jeans don't fit over BBB. Maybe they would be good for night times on a NB though. But i have also heard that tucking the frills around the legs in stops leaks for little ones.
We have BBBs and BBHs and BBBs are def my fav. Yes they do take longer to dry, but the absorbancy factor out weighs that imo. I would like to see them in prints...!!
As for covers, i tend to use wool or fleece covers (which yes adds to the bulkiness) with these nappies mainly because they hold so much wee, and the risk of compression leaks (especially when travelling in the car).