I think the cropped image looks sharper. I agree.
When you resize are you resizing 1 dimension (the length OR the width)?
That's what you should be doing. Choose 1 dimension and let the other dimension fill in automatically. OR reduce the image by a percentage.
I think the key in your case has to do with ratio. The image, when reduced must be reduced so that the ratio is exactly the same. It may well be that your settings are set so that the program is adding pixels (interpolation, I think it's called) and there is no reason the image should get fuzzier upon reduction.
Feel free to PM me about this. I'm sure I can help you solve it.
this NEVER happens to me
hope that helps