How can I compare "Ode to a Nightingale" by John Keats to Shakespeare's A Midsummer Night's Dream?

A nightingale, as featured in A Midsummer Night’s Dream, has numerous connotations, on which John Keats also drew in his ode written two centuries later. The bird is beloved of poets because its lovely, distinctive song contrasts to its simple, plain appearance. It is especially appropriate for a play that takes place largely at night. In addition, Keats obviously drew on dialogue from William Shakespeare’s play.
One place that uses the bird in the play is in a scene where Titania, the fairy queen, demands that it sing to help her sleep (act 2, scene 2). Calling the bird “Philomel,” the fairies bid him to sing the queen to sleep:

Philomel, with melodySing in our sweet lullaby;Lulla, lulla, lullaby, lulla, lulla, lullaby:Never harm,Nor spell nor charm,Come our lovely lady nigh;So good night, with lullaby.

In a comic vein, when the rustics gather to rehearse their upcoming performance of Pyramus and Thisbe, Bottom clamors to play the Lion as well as Pyramus. The reason for this is that he wants to roar. The comedy here arises from the contrast between the bird’s sweet song and the bellowing noise Bottom is making. He states that he will roar gently (like a dove) so he doesn’t frighten the ladies.

Let me play the lion too: I will roar, that I will do any man's heart good to hear me; I will roar, that I will make the duke say 'Let him roar again, let him roar again.' . . .
I will aggravate my voice so that I will roar you as gently as any sucking dove; I will roar you an 'twere any nightingale.

Oberon’s speech (act 2, scene 1) describing the woods appears to have especially inspired Keats, who also mentions the violet, musk-rose, and eglantine.

I know a bank where the wild thyme blows,Where oxlips and the nodding violet grows,Quite over-canopied with luscious woodbine,With sweet musk-roses and with eglantine:There sleeps Titania sometime of the night,Lull'd in these flowers with dances and delight . . .

While there are numerous differences, both the flowers mentioned and the overall sylvan enchantment of Keats’s work are clearly modeled on the speech above.

I cannot see what flowers are at my feet,Nor what soft incense hangs upon the boughs,But, in embalmed darkness, guess each sweetWherewith the seasonable month endowsThe grass, the thicket, and the fruit-tree wild;White hawthorn, and the pastoral eglantine;Fast fading violets cover'd up in leaves;And mid-May's eldest child,The coming musk-rose, full of dewy wine,The murmurous haunt of flies on summer eves.

Themes of illusion, sleep, dreaming, and other nocturnal associations also join Keats’s work with Shakespeare’s play. When the bird’s song ends, the speaker in the poem does not know if he really heard it.

Up the hill-side; and now 'tis buried deepIn the next valley-glades:Was it a vision, or a waking dream?Fled is that music:—Do I wake or sleep?

The connections between these works were explored by Joseph Candido in the 1970s.
https://www.poetryfoundation.org/poems/44479/ode-to-a-nightingale