The first thing of note in reading Spenser's Amoretti Sonnet 75 and Shakespeare's Sonnet 18 is that Spenser's conjures a deeper image of actual address between two people. Part of this is because the lady does appear as a speaker in Spenser's Sonnet 75 whereas Shakespeare's Sonnet 18 is one speaker, which conjures an image of musing or writing in solitude. Another reason is that, linguistically, Spenser's opening lines use brighter sounding vowels whereas Shakespeare uses more somber sounding ones.
In comparison, both poets end their fourteen-line sonnets with the genre definitive rhyming couplet, however Spenser uses an approximate rhyme (subdue/renew), whereas Shakespeare uses a perfect rhyme. Thematically, both poets sing the same song, so to speak. Each poet declares that the sonnet written in celebration of the beloved one will cause her to live on eternally on earth because "So long as men can breathe or eyes can see," so long will their sonnets be read. So far, they've both been right.
One thematic difference is that in Spenser's, the fair lady chastises him for trying to immortalize that which is mortal flesh and blood and must decay. In Shakespeare's, he addresses the argument of fading and decaying by talking about it himself: "And summer's lease hath all too short a date." Through two different methods, both poets bring up the idea of the short life span of mortality.