How would I compare Robert Frost's two poems "Birches" and "Stopping by Wood on a Snowy Evening"?

Well, one way of drawing a comparison between these two
excellent poems would be to consider how both poems present earthly cares and duties and
the speaker's attitude towards them. Note what the speaker in "Birches"
says:

I'd
like to get away from earth awhile

And then come back to it
and begin over.

May no fate willfully misunderstand
me

And half grant what I wish and snatch me
away

Not to return. Earth's the right place for
love:

I don't know where it's likely to go
better.

Thus we see that
after the speaker desires to get away from earth for a while metaphorically by climbing
the birches and swinging on them, the speaker clarifies that he is not wanting a
permanent escape, like death. He just wants to experience a temporary break from earthy
responsibilities and cares.

We see this theme evident in
"Stopping By Woods on a Snowy Evening" as well, as the speaker is entranced by the
beauty of the woods and almost overcome by a desire to stay there, enjoying the sight,
but reluctantly feels the pull of various commitments dragging him back to reality. Note
what the final stanza says:

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The woods are lovely, dark, and
deep,

But I have promises to
keep,

And miles to go before I
sleep,

And miles to go before I
sleep.

The speaker thus
desires the same kind of break and freedom from responsibilities that the speaker in
"Birches" does, but even though the woods are described as being so attractive, the
speaker reluctantly realises that he has "promises to keep" in the form of various
commitments and responsibilities that he cannot dispense with just yet. The repetition
of the final line suggests the speaker's weariness at the thought of the "miles" that
lay before him.