When I think I'm going to spend a lot of time in the hammock or when the weather is colder on a camping trip, I take the Blackbird because I'll have more stuff in the hammock with me and like having the pocket and netting to keep things from dropping on the ground.
If I don't think I'm going to spend a lot of time in the hammock or wanting to go lighter I take the Traveller with bugnet.
I got the Blackbird with 1.1 double layer and straps and then the Traveller with single layer and I put whoopie slings on it so there is a weight savings with my setups. It's about a pound lighter so a decent savings when you're counting ounces.
I intend to live forever, or die trying. -- Groucho Marx (1890 - 1977)