Shadows Against Paper

I'm working a project where some art is being provided in the form of page-size Photoshop files that are largely transparent. There is a significant shadow on one of the elements. I have been surprised by the perceived change in the intensity of the shadow when the image is placed into InDesign.

Here's what I'm talking about in pictures:

    

These are two pictures of the same shadow. On the left, you can see how it looks in Photoshop against a transparent background. On the right, is the same shadow placed on a "white" page in InDesign (actually, it looks exactly the same as it does in Photoshop when a white background layer is activated behind the shadow -- this is actually what I did to capture this image).

I'm not quite sure where I'm going with this! The questions I'm grappling with are:

1. If I place the transparent image in InDesign, does the document benefit given that doing so results in a much larger document that takes considerably longer to process, thereby slowing down my InDesign activities.
2. If I place a flattened version of this in InDesign, should the image occupy the full page or should I size it to eliminate the tracts of white that cover most of the page?

I'm leaning towards flattening but retaining the full-page coverage. During earlier work where I had optimized the size of the image, I had some problems with other shadows that crossed the boundary.

I'm going to come back to this article with examples of those issues, but for now, I'm moving forward with flattened, full page images.