In "To a Skylark" by Percy Bysshe Shelley, how are our songs different from those of a skylark?

Basically, the skylark's songs are happier than ours.

The speaker opens the poem by calling the skylark a "blithe Spirit," and spends a great deal of the poem describing the pure happiness that the bird's songs express.

The thirteenth and fourteenth stanzas specifically compare the bird's songs to our human songs, emphasizing how ours aren't as happy:

Teach us, Sprite or Bird,What sweet thoughts are thine:I have never heardPraise of love or...

Basically, the skylark's songs are happier than ours.

The speaker opens the poem by calling the skylark a "blithe Spirit," and spends a great deal of the poem describing the pure happiness that the bird's songs express.

The thirteenth and fourteenth stanzas specifically compare the bird's songs to our human songs, emphasizing how ours aren't as happy:

Teach us, Sprite or Bird,
What sweet thoughts are thine:
I have never heard
Praise of love or wine
That panted forth a flood of rapture so divine.

Chorus Hymeneal,
Or triumphal chant,
Match'd with thine would be all
But an empty vaunt,
A thing wherein we feel there is some hidden want.

Above, in the thirteenth stanza, the speaker is asking the bird what it is he thinks about that makes him sing so happily. Although we humans might sing pretty happily about love or about wine, the speaker explains, we still don't end up with songs that are so full of "rapture" (meaning intense delight or enthusiasm) like the skylark's are. And in the fourteenth stanza (also quoted above) the speaker continues the comparison, saying that even our wedding songs ("Chorus Hymeneal") or our chants of victory seem like just empty bragging in comparison to the skylark's pure, happy songs.

The speaker attempts to explain, toward the end of the poem, why our human songs aren't pure expressions of joy like the skylark's:

We look before and after,
And pine for what is not:
Our sincerest laughter
With some pain is fraught;
Our sweetest songs are those that tell of saddest thought.

This means that we think about the past and the future, and we wish for whatever we don't have, and because of that, even when we laugh we're still experiencing some kind of sadness. So, those mixed emotions come out in our songs, making even our happy songs pretty sad.

Finally, the speaker decides that if the skylark could share what he's so happy about, then we humans could sing songs of our own that are so joyful that they command attention, like the skylark's songs do:

Teach me half the gladness
That thy brain must know,
Such harmonious madness
From my lips would flow
The world should listen then, as I am listening now.