Hammock has the advantage when wild camping of not requiring flat ground, on many a trip I've cursed not having a hammock as I've had to cycle considerably further to find somewhere flat to roll out my bivvi bag. Conversely, it does tend to require trees...
The main downside of a hammock is that the insulation to make it comfortable is heavy and bulky. Typically as well as the hammock you're looking at an under quilt for under insulation, as well as your sleeping bag or top quilt. On top of that if you go the DD route of a travel hammock that you can use on the ground, then you are then also looking at carrying a sleep matt as well! It gets bulky and heavy fast. That said one of the female competitors of the TCR 2016 used a hammock and it seemed to be very effective.
Personally unless I'm using official campsites*, or going somewhere I'm expecting substantial storms or wind, I go for a bivvi bag and tarp. If I'm going really light it's about 500g for my shelter (200g for the tarp, 250g for the bivvi, 50g for the pegs). But that doesn't include poles, and relies on handy trees. I do have a set of poles, but they add about 100g to the setup. If I'm after a bit more comfort rather than weight savings, then I use a 500g bivvi bag instead. I can fit everything I need for a night out wild camping, including an evening meal, stove, and something to cook it in, in my 15l backpack. With some origami, it fits in my 16.5l saddle pack.
J
* I have used the bivvi+tarp option on official campsites a couple of times, the main issue you run into is people asking "Wait, you slept in that?!". That and trying to get into clothes inside the bivvi bag, as when you weren't awake last night you stripped off to sleep, and now it's day light...