As with property values, attractiveness is mostly in the eyes of the beholder.
By some objective definitions, however, it can be fairly said that natural yards are more attractive than lawns. For example, an idea called Attention Restoration Theory suggests that we inherently prefer to look at plants growing in their natural forms. Under this theory, humans like to look at plants, animals, clouds, water, and other natural things, because those are the kinds of things we evolved to look at. Hence, our brains are good at looking at those kinds of things, and we find these scenes mentally restful.
In contrast, our brains are not good at dealing with cars, ATMs, microwaves, DVR remotes, and all the other trappings of modern life. Looking at unnatural things is mentally tiring, leaving us with fewer resources for activities like learning difficult material, paying attention to boring tasks, and staying calm in stressful situations. Looking at nature, Attention Restoration Theory concludes, gives our brain a break, and helps us recover our full capacities.
When people say that humans find lawns attractive, they tend to invoke a different evolutionary theory: the idea that lawns resemble our ancestral habitat. In fact, there is little evidence to support the notion that humans evolved around very short grass. (Grass as short as a typical lawn does not even exist anywhere in nature.) On the contrary, humans evolved on the savanna, an ecosystem dominated by grasses about three feet high.
Current leading research on human evolution says that we are creatures of tall grass; we even owe our bipedal stance to tall grass. On the savanna, not being able to see over the grass is a big disadvantage. Many grassland animals dealt with this problem by evolving longer legs or necks, but humans did it by unfolding themselves and starting to walk upright.
Setting aside the evolutionary theories, it could also simply be said that natural yards are more interesting to look at. They are more diverse. They change over time. Plants move in the wind, and animals move among them. Walking through a natural yard tends to reward the visitor with the opportunity to see things that were previously hidden.
A lawn, in contrast, remains static across days and seasons and years. It generally includes little activity, and walking across it doesn’t bring into view anything that couldn’t be seen from the original vantage point. If the word “attractive” describes something that draws you towards it, then a healthy plant community certainly embodies this characteristic more than a flat monoculture.