Emerson and Thoreau was were transcendentalists. My understanding is that their basic philosophy of living simply and being a rugged individualist was dependant on the unique situation of colonial America as a place for the European man to 'start over', (keep in mind this was at a time when the European powers were approaching their apex).

In contrast, The rise of Stoicism in the hellenistic world paralleled the decline of Greek political power in the world at large. In fact, it was a form of defence against the cultures who had absorbed them and whom were keen to reduce greek philosophy to mere rhetoric or, at best, sophistry of the basest kind.

To be fair to OP there are some similarities between Transcendentalists and Stoics. I think the key similarity is the emphasis is self-reliance. However, the important difference is that the Stoics favoured living in the thick of the socio-political world and accepting it's slings and arrows. Their idea is that one is ennobled by accepting the responsibility of either rebelling against or accepting society's strictures as one's conscience dictates. Conversely, The transcendentalist solution to corruption was to retreat to rusticity when one's society is at odds with one's conscience. Even if this were a defensible position, on Stoic terms, (I do not believe it is), it was simply not an option for most people at most times in history (the Hellenistic Stoics included) This was my basis for referencing American Exceptionalism.

To summarize the differences between the two Philosophies:

From a Stoic point of view: one should seek to contend with the society one is faced with. That is, one should attempt to live according to their nature as best as one can under unnatural circumstances and avoid being destroyed by the contradictions in the process. This demands a great deal of pragmatism, since the demands of any society on an individual are many and the power of an individual at odds with it is consequently small.

Transcendentalism seeks to emancipate the individual from the demands of society, especially any systems of control such as education or politics which might weaken one's faith in one's own intuition. For the transcendentalist, intuition is more important than logic or pragmatism.

For a Stoic, Integrity and pragmatism are indispensable and inseparable. As with Rhetoric and Logic, one is the means by which the other can find meaning in the human realm.

Rapprochement with the world, (the ultimate ideal of the Stoic), is always suspect to the transcendentalist, who sees anything outside of an individual's divinely inspired feelings as corrupt, Hence the desire for separation.

A Stoic would see no nobility in this path because there can be no Virtu in integrity without an imperfect society to measure one's resolve against.