I would suggest that their primary similarity is that both thinkers believed in the idea of individuals engaging in self- definition through their own emotional states. In his essay on Self- Reliance, Emerson writes that "imitation is suicide." Such an idea is rooted in the belief that individuals have to hear their own voice and listen clearly to what is present in their hearts and minds as they engage in self definition. They will not be able to follow others as a blind herd in order to define themselves. In the same light, Thoreau believes passionately in the idea of staying true to one's own conviction as one engages in self definition. I think that this is critical in his writings and can be seen in his opposition to governmental action, such as the Mexican- American War. The need to define oneself through action and rebellion, listening to one's heart and mind as opposed to blindly following the state, is of critical importance to Thoreau.
To me, the major similarity between the two is that they were both Transcendentalists. Perhaps the most important belief of the Transcendentalists was the idea that people should adhere to their own consciences and not worry too much about what society thought they should do.
This idea can be seen in both of the works you mention. You can use the famous quote from Emerson that "whoso would be a man must be a nonconformist."
From Thoreau's essay, a good quote that represents this idea (assuming that you don't need anything very long) is
The only obligation which I have a right to assume is to do at any time what I think right.
These quotes make clear that both men felt that people should obey their own consciences, and not the dictates of society.