I understand the sentence, but what I'm trying to understand is why the information removed is (significantly) different - since they're both perceptual codecs, there should be a large overlap in what is removed from the output.
Eg, take a frame which has a solid chunk of blue. Codec 1 removes some of data to make things more consistent and then compresses it. Codec 2 looks at the output of codec 1, sees the consistently large blue area, doesn't see any info worth removing, and compresses it.
I don't know all the maths behind it, but try saving a JPG, close it, open it, save it again, repeat a few times. You'll see quality degrade every time you close it. My guess is that the lossy compressors try their best to preserve the previous compression artifacts, but in doing so they introduce more compression artifacts.
Eg, take a frame which has a solid chunk of blue. Codec 1 removes some of data to make things more consistent and then compresses it. Codec 2 looks at the output of codec 1, sees the consistently large blue area, doesn't see any info worth removing, and compresses it.