What is the difference in power consumption between these two RGB LED circuits, one common cathode, the other common andode?
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.