The main language difference between the first two scenes of Shakespeare's A Midsummer Night's Dream is that the first is written in verse and the second in prose.
Scene 1 contains this speech of Hippolyta's:
Four days will quickly steep themselves in night,/Four nights will quickly dream away the time;/And then the moon, like to a silver bow/New-bent in heaven, shall behold the night/Of our solemnities. (lines 6-10)
Her language is a poetic one, rich in similes and personification.
Scene 2 has these words of Peter Quince's:
But masters, here are your parts; and I am to entreat you, request you, and desire you to con them by tomorrow night; and meet me in the palace wood, a mile without the town, by moonlight. There will we rehearse; for if we meet in the city, we shall be dogged with company, and our devices known. (lines 88-94)
His directions to his fellow thespians are purely prosaic, a mere list of instructions.
Scene 1 (lines 134-140) boasts this exchange between Lysander and Hermia:
Lysander: The course of true love never did run smooth;/But either it was different in blood -
Hermia: O cross! too high to be enthralled to low.
Lysander: Or else misgraffed in respect of years -
Hermia: O spite! too old to be engaged to young.
Lysander: Or else it stood upon the choice of friends -
Hermia: O hell! to choose love by another's eyes.
Lysander's and Hermia's lines romantically intertwine, as if being spoken by one empathetic voice full of elegance and symmetry.
Scene 2 (lines 36-42) has this dialogue between Quince and Flute:
Quince: Francis Flute the bellows-mender.
Flute: Here, Peter Quince.
Quince: Flute, you must take Thisby on you.
Flute: What is Thisby? a wand'ring knight?
Quince: It is the lady that Pyramus must love.
Flute: Nay, faith, let me not play a woman. I have a beard coming.
The back-and-forth between these two "rude mechanicals" is characteristic of the language of the scene as a whole: earthy and straight-forward. There are no frills here.
A second difference in the styles of the two scenes is in the length of the lines. In scene 1, the characters, for the most part, make long rhetorical speeches. Egeus's speech to Theseus (lines 22-45) is a good example, as are Lysander's (lines 99-110) and Helena's soliloquy (lines 226-251). In scene 2, the characters -- with the occasional exception of the egotistical Bottom -- speak to each other in relatively short exchanges, (lines 1-20, for example).
Shakespeare continues this contrast in styles -- poetry for the lovers, prose for the laborers -- throughout the play, until the two linguistic worlds collide in the final scene. Ironically, in this last scene (V, 1), the "mechanicals" get to speak the poetry (albeit bad poetry), and the lovers speak primarily in prose.