If I could only have one, paracord wins hands down.

But keep in mind that it is possible to build a leanto with neither of them. Find two trees side by side about a foot (or more) farther apart than you are tall, with branches at about the same level above the ground. Put your ridgepole into the fork of those branches. Then cut some branches long enough to extend from above the ridgepole to the ground at an angle, and leave a smaller branch sticking out enough to hook over the ridge pole. Do a bunch of those close together, then add more layers and you have your leanto...