"Power consumption of common cathode is lower than common anode about 30%"
Is it right?
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Is it right? No it is not
It is utter nonsense stated by someone who obviously knows nothing about LEDs and/or electronics.
From the LED's point of view, they don't even "know" how they're connected.
Maybe the person who made the statement compared a 20 years old common cathode to a brand new common anode. Sure in 20 years LED efficiency has improved but that is unrelated to the way the LEDs are connected.