Welcome to the forum @Ewout
Good question! The response is not obvious. I think almost all scientific circles reason in terms of power / wing area ratio, following the seminal Loyd’s publication: Crosswind Kite Power.
On this criterion, crosswind flying wings are much superior to parachutes, according to a lift to drag (L/D) squared ratio. This ratio still increases when the wing is rigid, leading to increasing of the L/D ratio.
Now if power / weight aloft ratio is applied, things are different.
And now if Power to space use ratio is taken into account things can be still different: the path of a crosswind (above all rigid) kite is far larger than the useful swept area (being able to be the parachute area) due to the flight requirement; and within a kite-farm very large spacing between unities (and also the inhabited areas) is required due to safety needs as they fly fast.
So in the end a kite-farm using parachutes flying slowly could be denser…