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You could do it either way, but it is usually better to apply effects that depend on the size or resolution of the picture on the final-sized picture.  This is assuming, of course, that proper anti-aliasing is always done along with any resolution reduction.

The visual effect of blurring is dependent on the resolution and also the final viewed size of the image.  It is therefore more straight-forward to apply such effects on the final-sized picture, because that's the only place the result can be judged.

Note that effects that do not depend on resolution or viewing size (like color balance, for example) are best applied to the highest resolution possible.  Any manipulation of the original can introduce quantization and other noise.  If applied to the full res picture, the filtering process to shrink to the final resolution provides some attenuation of that noise.  In effect, you are using the higher spatial resolution in the original to get more color resolution in the final version.