Can you compare and contrast Shakespeare's Sonnet 130 and Petrarch's Sonnet 90?

There are some general similarities between these two sonnets, though there are more, and more substantial, differences between them. Poetic analysis covers every particular of poetry from structure to literary techniques and all that lies between. Because of the limited format eNotes offers, it will not be possible to give more than a general comparison of general analyses.

The first difference is in structure. Petrarch, who originally developed the sonnet form, structured this sonnet as one octet (8 line stanza) followed by one sestet (6 line stanza. Petrarchan form requires 14 lines in sonnets. Shakespeare, who learned the sonnet form from the adaptations to Petrarch's form innovated by Wyatt and Surrey, structured this sonnet as three quatrains and one couplet (couplets always have end-rhymes). Rhyme schemes for each form also differ: Petrarch, abbaabba cdedce, with a concatenated (linked) aa couplet at lines 4 and 5 resulting in a total of three couplets; Shakespeare, abab cdcd efef gg, with only one end couplet.

One similarity is that both sonnets speak of love that has lost the luster of beauty, in fact, Shakespeare speaks of love that seemingly never had the luster of beauty. One difference is in how the poets speak of this presently lusterless love. Petrarch speaks with saddened love and fond remembrance saying that though the bow is Cupid's arrow is no longer "bent" by his beloved, the "wound" of Cupid's first arrows still is active: he still loves her as though she were what she once was.

She did not walk in any mortal way,
But with angelic progress; when she spoke,
Unearthly voices sang in unison.

Shakespeare speaks of his lusterless love with biting irony calling froth images of beauty that she is or has not and comparing her to what she is not. His paradox in the resolving couplet states his adamant acceptance and admiration of her notwithstanding missing luster.

And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
[...]
   And yet, by heaven, I think my love as rare
   As any she belied with false compare.

How do the themes, tones, and forms of Sonnet 130 by Shakespeare and Sonnet 90 by Petrarch compare?

Both sonnets address the subject of lackluster love: love that continues even when the beauteous luster of the beloved has worn off ... or was never there. The thematic approach Shakespeare takes to this subject is to describe his beloved in terms of what she is or has not. This thematic approach is made dramatically clear in the first two negative lines:

My mistress' eyes are nothing like the sun;
Coral is far more red than her lips' red;

The thematic approach Petrarch takes is to recognize, seemingly in response to anothers' comments, the loss of loveliness his beloved has experienced due to time and/or troubles. Lines 3 and 4 of the octet clearly illustrate this approach:

Her eyes were brighter than the radiant west.
(Seldom they shine so now.)...

The tone the poetic speaker, who is assumed to be the poet in sonnets, takes in Shakespeare's Sonnet 130 is decidedly ironic and frank yet adamantly accepting and admiring:

IRONY: And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
ACCEPTING/ADMIRING: And yet, by heaven, I think my love as rare
As any she belied with false compare.

The tone in Petrarch's Sonnet 90 of his sonnet cycle of 317 sonnets to Laura (part of Petrarch's more extensive Canzoniere) is more complex. It is affectionately fond, slightly defiant ["("It was false pity," you would now protest.)"] and sadly reminiscent of past youth and love:

... You say she is not so today?
Well, though the bow's unbent, the wound bleeds on.

The two forms are different representations of sonnet structure. Bear in mind that Petrarch originated the sonnet form and then Shakespeare took up the variations to that form; these were innovated by Wyatt and Surrey (Henry Howard) as an accommodation to the English language. Petrarch's sonnets are formally structured as one octet followed by one sestet (one 8 line stanza followed by one 6 line stanza). Wyatt and Surrey innovated, and Shakespeare adopted, a formal structure of 3 quatrain stanzas (4 lines each) followed by a couplet (couplets by definition are two lines with end-rhymes). The total number of lines for each structural form is 14. 

Shakespeare utilizes the quatrain/couplet form to introduce three topics related to the subject: what she has/is (Q 1); what he has seen/smelled (Q 2); what she is negatively compared to ("music" "a goddess") (Q 3). The couplet resolves the paradox he develops in the quatrains, which may be stated as: My love is unlovely.

Petrarch utilizes the octet/sestet form to develop his experience of her in the octet

I had love's tinder heaped within my breast;
What wonder that the flame burnt furiously?

and to develop her youthful characteristics in the first four and a half lines of the sestet

She did not walk in any mortal way,
But with angelic progress;...

The last two lines of the sestet provide the metaphorical paradoxical resolution to the contrast developed in the preceding lines: [paraphrase] though she no longer has the power to charm and drive Cupid's arrows to his heart as she did in past times, the effect of Cupid's arrow still is an active one:

... You say she is not so today?
Well, though the bow's unbent, the wound bleeds on.

One point to note is that though both forms structurally depend upon a resolving paradox, Shakespeare's form resolves, in the couplet, a previously developed paradox, while Petrarch's presents a paradox as the resolution to contrasts previously developed. Yes, both relate to the resolution, but the quatrain/couplet builds then resolves a paradox while the octet/sestet offers a paradox as the resolution: there is a paradox then a resolution (couplet) versus there being a contrast then a paradox (ending of sestet).