Well after reading so eloquent and well thought out a backing for bicubic I went back yet again to test my findings to see if I could have been somehow missing something and lo and behold I was. I really must say that I have to now concur with Rico. I'd post my test results but for the fact that they would be rather mundane. Suffice to say, when downsizing unexposed sheets of scanned sheet film, bicubic really is more than adequate.
I am perfectly aware that sinc functions lobe into negative coefficents outside the pi/2rad cut-point and creates "oversharpening" by up to 3% of the original contrast value (with lanczos windowing)... This is a single overshoot, to get "radiating lobes" you have to use a really crappy implementation of the algorithm. For a single resample down operation, I find this better than loosing 20% of the original contrast information (as bicubic does)... Those 20% are the negative effect of "no ringing" with a convolution window that's too narrow
How much "ringing" do you induce when sharpening this back to form? To make the average look good, you have to sharpen by an amount that creates LOTS of ringing (overshoot, or halos, or whichever term you choose to use) in some parts of the image, and too little in some... This means that you have to redo the "creative sharpening" PP all over again - and with much less detail than was present in the original (please distinct between detail and edge acuity - they're not the same!). By doing this you make sure ( ) that the new picture you have created will have very bad correlation with the original image.
One of the problems with sharpening a bicubic transform is that you CAN retrieve edge acuteness, but you can NEVER accurately retrieve balance or spatial accuracy in lost detail. I almost never find myself in need of sharpening a downwards resample with lanczos, having to do so would take a REALLY blurry original, which I had probably thrown out from the batch in the first place.
It all comes down to personal preference, or what "effect" you want to achieve. I prefer to achieve no effect at all, just a smaller picture - with one operation. But that might just be me.
) that the new picture you have created will have very bad correlation with the original image.