[LATER EDIT: I replaced the 1000px resizes with 920px resizes for more useful matching with some later images.]
TEST: Downsize the 7360 x 4912 px Siemen's Star to 1000px 920px width with no new sharpening after the downsize.
Photo 1 :: Capture NX2 downsize to 1000px 920px width with no new sharpening after downsize.
Photo 2 :: Photo Mechanic downsize to 1000px 920px width with no new sharpening after downsize.
Photo 3 :: Photoshop Elements 11 downsize to 1000px 920px width with no new sharpening after downsize.
CONCLUSION ::
On a Macbook Pro Retina screen, the downsize in Photo 3, made with PSE Bicubic Sharper, retains more center detail.
The downsizes made in NX2 and Photo Mechanic have both lost some center detail.
The Capture NX2 downsize is a bit better than the Photo Mechanic version.
Count the rings from the center to see that the NX2 downsize loses large amounts of detail in the first 3 rings,
while the PhoMechic downsize loses detail in the first 4-4.5 rings.
ADDED LATER: Actually it is not center detail that we should worry about so much. We know we are going to lose center detail in this kind of star with tiny 1-pixel frequency detail. What happens in the slightly larger areas is what we want to look at I think.
Note :: Be sure to expand your browser so that you can view the full 1000 920 pixel width.
Right-click the photo and select View Image Info to verify this by checking that the displayed dimensions are 1000 x 667 px 920 x 614 px.