Beautiful piece, one of my favourites!
The answer to your question is… neither! You actually share the broken chords between both hands.
There are three distinct parts (voices) on this piece: The top melody, the bass and the middle broken chord accompaniment. The melody is played with the 4-5 of the right hand, the bass is played with 4-5 of the LH, and the broken chords are played by both RH and LH using fingers 1-2-3.
Consider the first bar:
Top voice (RH): G(5)- G(5) – G(5)- G(5)
Middle voice: LH - Bb(2) Eb (1) then RH - G(1)-Bb(2) then LH - Bb(2) Eb (1) then RH - G(1)-Bb(2)
Bass (LH) Eb (5)
I suggest you learn this piece by first completely ignoring the middle broken chord voice and simply play the melody and the bass (using the final fingering you will eventually be using). Then learn just the broken chord accompaniment (again using the final fingering). Once both these parts are ingrained, join them.
Best wishes,
Bernhard.