Question about the size of HDR probes

I’ve tried to render a big scene using a very big HDR probe (2048 x 2048, 9 MB) but Blender crashed every time because I didn’t have enough memory to handle both.

So, I resized the probe (with HDRShop) to 512 x 512 (600 KB) and made a few test renders. I was expecting a drastic change in luminosity, but the results were (as far as I noticed) the same (click image):

In what case would somebody need such a big probe? (besides a rectal examination)

Why should there be a difference in luminosity? o.O

And why to use a high-resolution background? Well for detail of course…
but that sky indeed doesn’t seem to have much detail anyway, at least in the part visible here.

Lynx, please don’t answer a question with another question.

I thought luminosity would decrease because a 512 pixel image would contain less information than a 2048.