I think the formulation is changed (as when you do a simple F.E. calculation on paper with small deformation and neglect 2nd+ order parts in your integration).
Plus, using large deformations, your load (only if you apply a pressure), can follow your deformation.
For example, say you model a 3D beam along X axis. The "vertical" is along the Z axis. You define a section at the end of your beam to apply a load along Z axis.
If you don't take large deformations into account, your load will be along Z axis even at the end of the study, whatever the deformation is.
If you take into account large deformations and use a force / remote force / nodal force, the load will still stick to the Z-axis, but if you use a pressure instead, the resultant load will be normal to the area of application of the pressure.
This is why a solve often uses iterations when taking large deformations into account.
(This part at least is explained briefly in the Ansys help)