It is a different spread of light in diffuse surface some scenes will have more contrast some others less, others will change a very bit, all will depend in the amount of very rough surfaces you have in your project. here are some examples.
In this kitchen the oren nayar version is this.
and this is the non oren nayar version.
the next are other scenes I tested with oren nayar.
oren nayar.
non oren nayar.
Oren nayar.
Non oren nayar.
Maybe you will think there’s no so much difference, but all those scenes are made without knowing about oren nayar and how diffuse work in others renderers, so I made all materials to look well using lambertian, maybe making a scene from scratch using oren nayar will show better it’s benefits.
but in general what we can find is that oren nayar change how the light it’s spreaded in a scene, and in almost all scenes gives a more deeper light fallof, you can see how lambertian make the light look like it’s very linear while oren nayar make it look like it’s less linear and more soft, also in some scenes you gain more light info like the first kitchen example.