The two poems demonstrate different views of life and the impact it makes on an individual, as well as the impact an individual makes one the world.
“The Brook” can be seen as a metaphor for the insignificance of each individual person. We all go through life and make our mark, but in the grand scheme of things the world goes on even after we go.
I chatter, chatter, as I flow
To join the brimming river,
For men may come and men may go,
But I go on for ever.
The river can be a metaphor for Heaven or death. Everyone is born and dies.
Unlike the brook, which has no choice, in “The Road Not Taken” the speaker has a choice. He is faced with two roads, and decides to take one that fewer people have taken. He is a visionary, or a rebel.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.
Whether this was successful for him or not, the speaker clearly felt that choosing the road he did made an impact on his life. He does not say that his choice made an impact on others or the world.
Frost and Tennyson both use nature as a metaphor for life, but the main difference between the poem is that Tennyson's speaker is a personified brook, and Frosts is an actual person.