Diction is the style of speaking or writing and the choice of words used. Diction can refer to whether a poem is formal, informal, colloquial, or uses slang. Formal diction tends to be deemed more serious, but the Romantic poets tried to use more informal diction to make serious statements about poetry and life. The diction (style) of a poet might also have to do with his/her era or his/her particular subject matter and tone.
The tone and the poetic quality of this poem are very serious. But Frost does use simple or informal vocabulary to illustrate the simplicity of the theme: making difficult choices. He uses a formal style but with an informal landscape of the woods from which to derive the metaphor.
Stylistically and poetically, the poem is formal. This poem was written in 1916 when other poets were abandoning classic poetic words like "hence" and avoiding classic techniques like subject/verb inversion: "long I stood." Frost uses a balance of a classic-sounding style with simplistic and informal word choices. So, it is serious but accessible.
Some poets use "natural diction" which comes closer to natural speech. Here, Frost uses "poetic diction," that which more traditionally resembles poetic speech. Although the poem is about a natural and common event in life, Frost uses poetic speech to underscore the drama of his choice. For example, if he had opted for more natural diction in the last two lines, he might have said, "I will be saying this with a sigh / Sometime in the future."
Word choices are informal but descriptive. The style is formal and serious. Frost really stresses the seriousness in the final lines when he repeats the pronoun "I":
Two roads diverged in a wood, and I -
I took the one less traveled by,
And that has made all the difference.
He repeats the "I" to illustrate his hesitation and uncertainty, even in old age, that he will always be unsure if he had taken the road less traveled.