Oshyan, the default setting for Ray Detail Region already is "Detail in Crop Region". "Detail in Camera" is what you'd need if the region looks different when it's rendered cropped, i.e. you make it match the rest of the image by setting it to use the same detail region as the whole image ("in camera").
Lehm, the differences are probably due to Global Illumination. The Ray Detail Region will not help there. Increasing "GI sample quality" on the renderer should improve things, but watch out for how it affects render times and find a value that works for you.
Matt