In "Self-Reliance," Emerson's purpose is to argue that people need to avoid conformity. He argues that the only way to be a "man" is to do your own thing and to follow your own conscience. So the main point of that essay is that you do what you believe is right, rather than going with what society thinks.
By contrast, "Nature" is way more philosophical. In that essay, he's talking about how he believes that people and the universe are pretty much part of each other. And he's talking about his ideas about God and how we're all sort of part of God.
So the one is more of a argument about how people should live while the other is more of a philsophical discussion of the nature of the universe and of love and of God.
Emerson's essay "Nature" is an explanation of how humans and animals and plants are all part of the natural world, and within Nature is contained a beauty that also comes from people's response to its beauty and grandeur. Thus, "Nature" is an essay that proposes the tenets of Transcendentalism, the belief that man should enjoy an original relationship to the universe--indeed, an individual relationship with the universe. This contemplation of the majesty of nature can take a man by "surprise," and yet he can also know it.
Its effect is like that of a higher thought or a better emotion coming over me, when I deemed I was thinking justly or doing right.
This "higher thought of better emotion" can, then, certainly connect to the message of Emerson's other essay, "Self-Reliance." For, in this essay Emerson desires that each person find his/her own beauty and entertain his or her own higher thoughts and not compromise by becoming part of "the joint-stock company" of society that is in conspiracy against the individual. "Nothing is at last sacred but the integrity of your own mind." Each person is unique and has a distinct role to play in life, a role that he can discover in his contemplation in Nature. While Emerson does not explicitly state the connection between the individual and Nature as opposed to society, he does suggest that man can discover his individuality away from the conspiracy of society.