The canonical equipment for long bike tours definitely includes a tent. But sometimes it is a bit sad that we all use the same gear, the same brands: there should be more room for new ideas. Back in Ljubljana, I was advised to give hammock camping a try, so I got myself a DD Frontline Hammock and I tried it on my way back to France. As I had used a tent for the way to Ljubljana, I had to carry it too, so I was able to compare the two.
Let's start with the basics. My hammock weighs around 850g, whereas my two-person tent totals at 2kg. It's hard to compare these two figures because the tent accommodates two people and the hammock should be augmented with a tarp in order to be a real alternative to a tent (although that tarp would probably replace the mattress I need in the tent). But still, on a solo trip in a sunny country, the hammock is a no-brainer.
Hanging the hammock is definitely faster than pitching the tent, but again I should add a tarp for a fair comparison. Finding a place to hang the hammock is usually quite easy, but in many places I had the feeling that it was quicker to find a place to pitch the tent (given all the other constraints I have for wild camping places).
Sleeping in the hammock is very comfortable. You can see the nature around you (that's great!), but the mosquito net included keeps some warmth around you and create a bit of an enclosed space, which is nice. It is possible to have a look at your bike and bags from time to time, but they are a bit harder to reach than bags sitting in or around your tent.
One thing I really love about the hammock is that it does not touch the ground. So it remained clean throughout the trip and never got wet in the morning. In comparison, my tent rarely dries up by itself in the morning, even with good weather: there is always some humidity in the grass and from the condensation of my breathing. And I really don't like folding my wet tent into its bag: after a few days, the smell is not very welcoming.
So, all in all, I recommend hammock camping, especially on a solo trip.