I think it definitely depends.
How's that for helpful?
The following is all Ergo v. 4th Gen. Beco, as a) I haven't tried a BWD and b) the Ergo and 4th Gen. are more comparable.
The Beco is a bit lighter-weight overall, so that's good for people who like a carrier to be a bit lighter/less heavy than the Ergo. OTOH, some people prefer the heavier-duty Ergo.
The Beco has a very cool rolling-up strap so you can tie it up and leave it on around your waist when not in use.
A big difference is in body height. The Beco is taller than the Ergo, which is great for people with taller babies/toddlers, but people with shorter/younger babies may prefer the Ergo.
The waistband on the Beco is padded, but not quite as thick as the Ergo. Again, some people prefer one and some the other. One comment I have heard is that some people have a problem with the baby slipping into the waistband part of the Beco, that it doesn't always fit snugly enough.
The straps adjust differently -- the Beco has two-way adjusters, and the longest part pulls up towards your head -- you get more flexibility in adjustment but there's also more strappage flopping around, which some people don't like.
The hood design is definitely different. I love the pretty look of the Beco without the hood attached or with the hood tucked away, it's very nice, but frankly I think the hood of the Ergo functions better because it's attached to the carrier (the Beco hood only sticks on with velcro, one tug too hard and it comes off).
I think they're both great carriers, but I don't think one "wins" over the other overall -- it's just simply a matter of user preference and comfort (and appropriateness for your baby's size).