Here are two 100% crops...
Scroll them to the right to see those windows with white blinds:
real usable detail in 16.7mp 1Ds MkII files,
mushy moire in 22mp 5D MkIII files.
If you down-res the the 5DIII photo to match the 16.7mp of the 1DsII, it will look sharper. Or enlarge the 1DsII image to match the 22mp of the 5DIII and it will look less sharp. The 5DIII is presenting a bigger image of the same scene, so it looks less sharp. If you had a 36mp photo of the same scene and viewed it at 100%, it would look even less sharp. Also the unfortunate moire effect in the 5DIII photo is usually a result of greater resolution, not less.
This really makes no sense.
If I have tiny real details and texture in the white blinds on the windows in 1DsII sample
and I only have moire in the 5DIII sample,
why do you think that just
by downsampling the 5DIII file to 1DsII file size,
the detail that is not present in the 5DIII file will magically appear,
...or that just
by upsampling the 1DsII file to 5DIII file size,
the visible detail in the 1DsII file will magically disappear?

The resolved details are present in the files or they are not.
You can just try what you have suggested - use the crops that i have posted above,
resize them both way to match each other
and see if the lost details will appear in 5DIII file when you downsize it,
or if the fine resolved details will dissapear from 1Ds file by upsizing it.
Illusion of perceived sharpness achieved by stronger microcontrast is not the same as detail resolving ability.
1DsII files have both - more visible resolved detail
and higher microcontrast.
Remember that RAW files from both cameras were developed with the EXACT same settings,
so you can not say that file from one camera was sharpened more.
...
I'm a professional photographer for 20 years.
I have been shooting with 1Ds MkII since the day it was introduced
and I know every bit of its possibilities very well.
After all this years I wanted to upgrade to a more modern body.
I was hoping for a high MP body but we got 1Dx and 5DIII.
I (naively?) decided to try the 5DIII since it has more resolution
and the 1Dx is not good investment for my needs (studio) if the big MP camera is around the corner.
The moment I started using the 5DIII in the studio (100 ASA, etc),
I realised that I don't really like its RAW files compared to my old 1DsII files.
When I opened first 5DIII RAW file in Capture One (confirmed later in DPP and Adobe CR),
I thought for a couple of seconds that I must have missed the focus a little bit.
But I did not.
I was just used to the crispness and details in 1DsII files that are just not there in 5DIII files.
I was disappointed since
I wanted badly to like the 5DIII and to keep it for use in the studio.