In order to discuss whether Shakespeare's "Sonnet 73" and "Sonnet 138" are "anti Petrarchan," as your question suggests, we need to understand the commonly-used elements of a typical Petrarchan sonnet.

Aside from the differences in form of the Petrarchan and Shakespearean sonnets—octave/sestet of Petrarch and quatrains/couplet of Shakespeare—we can say that many of Petrarch's sonnets are addressed to the ideal conception of a lady, in the tradition of courtly love, and feature detailed descriptions of the physical beauty of the lady who is the subject of the sonnet; natural elements that complement her physical beauty; and, not least, the moral underpinnings of the lady's character that also make her desirable and unattainable. In short, her beauty is unmatched, and her character is unassailable.

In Shakespeare's "Sonnet 73," the theme is decay and the onset of old age, a theme that would not appear, especially in such graphic detail, in a Petrarchan sonnet. Shakespeare, as he does in Sonnet 138, focuses on age, but unlike Sonnet 138, the images are much starker and more threatening:

Upon those boughs which shake against the cold, / Bare ruined choirs, where late the sweet birds sang. / In me thou see'st the twilight of such day.

Shakespeare's use of "bare ruined choirs" is particularly effective because he alludes to the remains of churches and monasteries destroyed in the reign of Henry VIII, an image that would resonate with his lady because these decaying buildings litter the English landscape.

Continuing to focus on the real rather than the ideal, Shakespeare employs another image taken from nature to carry the theme of decay:

As after sunset fadeth in the west; / Which by and by black night doth take away, / Death's second self, that seals up all in rest.

Death's "second self" means sleep in this context, but, in the real world, this sleep is not temporary because it "seals up all" in the coffin and tomb in a permanent sleep. These images, as well as the theme itself, would not be employed in a typical Petrarchan sonnet.

These two sonnets explore themes very differently from the idealized world of the typical Petrarchan sonnet in that they center on highly-personal and realistic characteristics of human relationships—lovers overlooking their advancing age and lovers confronting the reality of decay and death. Indeed, the only commonality between these two sonnets and a Petrarchan sonnet is that they follow particular forms and rhyme schemes (but very different), but their approach to love, as a transaction between men and women, is vastly different.

Shakespeare's "Sonnet 138" is very different from a typical Petrarchan sonnet in that Shakespeare describes the real as opposed to the ideal. Rather than extolling the beauty and virtues of the lady, Shakespeare points out her flaws:

When my love swears she is made of truth, / I do believe her though I know she lies...Thus vainly thinking that she thinks me young, / Although she knows my days are past the best...

Shakespeare's observation here, of course, is not actually a criticism of his lady's honesty—she willfully convinces herself that, despite his age, he is young in her eyes—the intimacy of these lines, which deal with a loving kind of deception, is very different from the idealized relationships, which follow the elements of courtly love, in many of Petrarch's sonnets.

The closing couplet is typical of Shakespeare but would have seemed startling to a reader of a typical Petrarchan sonnet:

Therefore I lie with her, and she with me, / And in our faults by lies we flattered be.

Shakespeare continues his focus on the real, their faults, and, in an image that would have caused the reader of a Petrarchan sonnet to drop his or her jaw, Shakespeare says explicitly that "I lie with her,"—that is, they make love—an image that is distinctly not Petrarchan.