The Lumia 1020 has a 41MP sensor in a PHONE. It down-samples the photo to 5 megapixels, improving the photo quality. But would you get a better photo by using a native 5MP sensor of the same size?
In general, given two sensors of the same size, but with one of them having a higher resolution than the other, would the result of downsampling the higher resolution image to the lower resolution be better or worse than the image obtained from the lower resolution sensor?
(You can assume that a high-quality image downsampling algorithm is being used. And yes, a higher resolution photo gives you flexibility to crop, but for the purpose of this question, let's assume we are not going to crop the photo later.)
Answer
The pixel reduction from 41 to 8mp has the impact of improving the accuracy of colour capture and reducing the appearance of sensor noise since for each output pixel you've got a handful of pixels to calculate the best value. Obviously there's a tradeoff that you've got less spatial resolution and it comes down to what makes for the most pleasing image in the end.
Digital supersampling systems aren't new. Fuji's Super CCD cameras (like the 2002 S2 Pro which sampled 12megapixels but output at 6) were widely applauded for the quality of their colour reproduction/tonal range compared to their Nikon & Canon peers.
According to reviews the output between the likes of the Lumia 1020 and iPhone5 tend to be comparable under good lighting. But PureView devices generate better output in the kind of challenging situations where people are less likely to be carrying a camera with a larger sensor. In practice the whole system performs as well or better than a native 8mp sensor in a similar package.
The maths & physics involved mean that beyond a certain pixel density there are diminishing returns. Probably Nokia are very much at this point but the scope for improvement might be more about their processing than goosing the pixel density much further.
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