Heroic couplets
One of major differences between Jonson and Shakespeare was in what we might call their method and style. Shakespeare was incredibly creative, playful, and poetic. It's rumored that he never crossed out a line when he was writing. Jonson, on the other hand, was structured, rigid, and a super-revisionist, sort of like a well-honed poetry machine. Each created impressive pieces of literature, but they appear to have gone about it in very different ways and reached relatively opposite ends of the stylistic spectrum.
The form and meter of this poem are actually beautiful representations of both the contrast and the congruencies of Jonson and Shakespeare's respective works. Both, for instance, wrote their poetry primarily in iambic pentameter like Jonson uses here. Form-wise, however, Shakespeare opted to write in sonnet form. That's an older, inherently romantic style and one that, while still technically requiring a rhyme scheme and format, offers authors a lot of flexibility in terms of shaking up the meter and rhyming patterns.
Jonson's method of choice, however, was the heroic couplet, technically defined as rhyming pairs of verse in iambic pentameter. Take a look at these lines for an example:
To draw no envy, SHAKSPEARE, on thy name,
Am I thus ample to thy book and fame ;
While I confess thy writings to be such,
As neither Man nor Muse can praise too much.
See how perfect these first lines are? The whole poem is exactly the same way. Such style was in many ways pioneered by Jonson and required a painstakingly technical hand to work. (If you've ever encountered a slant rhyme in a poem of heroic couplets, you'll know what we mean; they are incredibly jarring.)
Heroic couplets become the poetry of the neoclassicists, and, largely thanks to Jonson, are associated with the kind of satirical, cynical, incredibly structured poetry that Jonson loves to write. The fact that here they are used in a more lyrical, poetic way (in tone much more similar to something Shakespeare wrote than most things in the Jonson canon) is beautiful testimony to Jonson's respect for the difference between himself and Shakespeare and also to his talent as a poet.