A lot of people really like the bugnet attatched to the hammock (WBBB) as it gives some "shape" to the footbox, you get the feeling of your feet being secured in and your TQ being secured.
That being said, I don't like the limited visibility as it is and I like to go without the bugnet I've learned if I don't have to.
With the BB though, you get a storage shelf inside the hammock you don't get with the Traveler, if that's important to you at all.
I think the Traveler Bugnet combo may possibly be lighter (I'd have to check, just assuming) since it has no zippers and the BB does.
Some things to think about while making your decision
"I ain't here for a long time, I'm here for a good time"
- George Strait