On the surface, these poems seem to have quite a bit in common. Both have a speaker who is solitary, alone in nature. Both indicate what time of year in which they take place: "The Road Not Taken" takes place in the fall, as we learn from the narrator's description of the "yellow wood," and "Stopping by Woods" takes place in the winter, as a deep snow falls. Both speakers have to make a choice: the speaker in "The Road Not Taken" must pick a road, now that he's reached a fork in it, and the speaker of "Stopping by Woods" must decide whether to stay in the tranquil wood or continue on to satisfy his obligations.
However, the motivations of these speakers seem completely different. The speaker in "Stopping by Woods" is drawn by the solitude he gets to experience in the quiet woods. He longs to remain in the woods which are "lovely, dark and deep" and full of "easy wind and downy flake." He seems to relish the tranquility and the quiet and calming sight of "watch[ing] [the] woods fill up with snow." He would stay, if he could. But, he has promises, obligations perhaps, that he feels he is bound to keep and a long, long way to go before he can rest. The speaker of "The Road Not Taken," on the other hand, has no doubt about whether or not he wants to keep moving; the question becomes, for him, which direction to go. Then, rather than reflecting on the appeal of tranquility and solitude, this speaker imagines a future in which he paints his decision as a great deal more meaningful than it actually is. He has said that the second road is "just as fair" as the first, and that "the passing there / Had worn them really about the same." In other words, they have been taken just about the same number of times by people who have come before. However, in the future, this speaker plans to tell this story, saying that he "took the [road] less traveled by" other people and that this decision "has made all the difference" in his life. Given what he's already told us about the equality of the roads, we know this to be a untrue.
Thus, the speaker in "Stopping by Woods" seems much more earnest: he is just a tired man appreciating the beauty of the nature around him and wishing for a break to stay and enjoy the winter scene. The speaker in "The Road Not Taken" harbors a desire to appear courageous and unique when, really, he has only made a decision that so many others before him have also made.
There is a strong similarity between Frost's "The Road Not Taken" and his "Stopping By Woods on a Snowy Evening." In both poems the speaker is on a journey and comes to a stop. In both poems he indicates the season of the year, which is fall in "The Road Not Taken" and early winter in "Stopping By Woods on a Snowy Evening." In both poems the speaker is all alone and seems to be having troubled feelings and emotions. Finally, in both poems the speaker (who is presumably Frost himself) has to move on because he cannot remain all alone in the woods. In "Stopping By Woods on a Snowy Evening" he moves on because he remembers he has obligations to fulfill, while in "The Road Not Taken" he moves on because he has to make a choice of one road or the other. There is very little difference in the motivations of the speakers in the two poems. The moods of both poems are very similar. The speaker seems lonely, puzzled, fascinated by the beauty of nature but forced to attend to the business of living.
Frost maintained that all writing, including poetry, should be dramatic. He makes these two poems dramatic by suggesting that the speakers both have internal conflicts. In "Stopping By Woods on a Snowy Evening" the speaker would like to stay by the woods much longer and enjoy the silence and the visual beauty. In "The Road Not Taken" the speaker would like to follow both roads but cannot do so because they "diverge" in entirely different directions.