To my knowledge, it's kind of hard to quantify exactly how much information is lost with a normal blurring algorithm (gaussian, box, etc), but it's usually less than you think. There are certain edge cases where no information is lost at all and the original image can be perfectly reconstructed if it's simple enough. Even if it's a normal photo of something complex, a deconvolution algorithm can work seemingly impossible magic on a blurry image without the need for an AI that will hallucinate details.

On the other hand, pixelating part of an image provably removes a large amount of information from that section of the image and no algorithm will be able to de-pixelate something without hallucinating details. Using a big box is the absolute best because it just deletes all information from that part of the image.

ETA: the problem is a lot worse in videos because you can use multiple frames with different offsets to reconstruct a higher quality image even if it's pixelated.

This would demonstrate it well with physical concepts

https://youtu.be/UpJ-kGII074?si=EoQQeplKXYj5kMT0

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