To analyze a poet's style, you'd start with structure because structure is part of a poet's style. You'd then examine diction by asking if it is formal, informal, or slang. You'd examine vocabulary to determine if it is simple or sophisticated. In other words and for example, does the poet call a rabbit a "rabbit," a "hare," a "wabbit," or "Oryctolagus cuniculus"?
You would examine syntax to determine the level of complexity. You would ask yourself questions like the following about syntax. Are simple, short sentences used? Are there any subordinate and coordinated clauses? Are there compound and complex sentences? Then you'd examine the text for poetic and rhetorical devices.
Some of these poetic devices might be imagery, metaphor, personification, irony. Some rhetorical devices might be the rearrangement of normal word order, e.g., "comes the knight here" instead of "the knight comes here"; ellipsis of words, e.g., the cat runs and so the bunny (the verb "does" is missing, or shows ellipsis); repetition of words or phrases, e.g., soon cometh June, soon cometh moon. There are many other of each, but these are common examples.
You would compare the analyses of the poems to find differences and similarities. I'll give some examples of the results of the compared analyses. "Loud Music" is written without stanzaic paragraphs: it is all one long block of verse. Most lines have enjambment. This means the thought of the line carries over without an end-stop (i.e., a period, colon, semicolon, emdash, or comma) to the next line or lines. For example, the "She is four" sentence has two lines of enjambment:
But my stepdaughter disagrees. She is four
and likes the music decorous, pitched below
her own voice-that tenuous projection of self.
In contrast, "Cartoon Physics, part 1" has many stanzaic paragraphs. Many are only one line long; most are two or three lines long. A good many of the lines have enjambment. In the example below, only one line has an end-stop, a soft comma end-stop after "wrecks":
should stick with burning houses, car wrecks,
ships going down -- earthbound, tangible
where they can be heroes. You can run
back into a burning house, sinking ships
Both poems are written in informal, conversational diction. Both use every-day vocabulary, but each also has a section or a stanzaic paragraph where the vocabulary is specialized. In "Loud Music," toward the end, the poet speaks of porpoise sonar and brooding creatures, while the subject matter is serious and straightforward:
and uses her voice as a porpoise uses
its sonar ...
as if some creature brooded underneath,
In "Cartoon Physics," The subject matter is serious but seems frivolous because of the deep, almost sarcastic, irony. The stanzaic paragraph with the specialized vocabulary is at the beginning:
Children under, say, ten, shouldn't know
that the universe is ever-expanding,
inexorably pushing into the vacuum, galaxies
swallowed by galaxies, whole
solar systems collapsing,