Water bending is derived from flow, the push and pull of water. Healing with water bending is allowing the body's natural chi to flow freely into damaged regions. Everyone has chi flowing from their seven chakras that act to naturally resist someone else manipulating them through bending. Bloodbending, requiring a full moon usually, is less a matter of realizing there is water in the body as it is overcoming the chi of the target. Tarrlok and his father Yakone could bloodbend at will, meaning they had a powerful ability to overcome people's chi to allow them to freely manipulate the water in their bodies. When Aang went into the Avatar State, he was no longer affected by this as his chi was off the charts. Amon is likely a very powerful nonbender with exceptional command of his chi, like the Guru.
Next, compare Aang's energy bending, when he permanently takes away someone's bending, to what Amon does.
Usually Aang is seen with his hand on the person's forehead and the other on his heart. Two chakras commanding Insight and Love respectively. It's likely Aang takes away bending by opening these chakras to insight and love where there was illusion and grief before. The True Mind and True Heart mentioned by the Lion Turtle, where the distinction and inner turmoil that fuels the bending of men like Ozai and Yakone disappear and thus takes away their bending.
Amon on the other hand touches a person's forehead and throat, which command Insight and Truth, and which are blocked by illusion and lies. Consider the possibility that Amon is not actually taking away a person's bending permanently, but instead corrupting their chakras into making them think they can no longer bend.