I had that concern too but the first backpack hunt I did was with a tarp and hammock setup. We just barely got camp set before it started raining. Over the next 12 hours it never stopped raining and there were several rounds of pretty heavy storms rolled through with lightening hitting all around us. Didnt have a single issue with gear getting wet. Sucked being stuck under the tarp that long but no worse than being in a small backpack tent for sure. We could at least standup, stretch and move some.I am not so sure about a hammock since I have never used one.
You still need to keep your stuff dry in rain or snow, so I think I would go with a tent.