A power supply of 10A is capable to supply more current than one of 6A. That is all.
The energy that is wasted depends on the quality and design. Some power supplies waste 50%, others only 2%.
The led shield seems to be able to supply 6*1A, that is a total of 6A.
But if 12V leds are used with a total of 6A, only 3A is needed from the 24V.
The swithing regulators are efficient because they can turn a high voltage into a lower voltage with more current.
I don't know what will happen if you connect more leds to one output of the shield. I have to know more about the shield to answer that question.
They look like PT4115 drivers (working on my own board using them) and I see that the seller also sells the PT4115 chip. They are buck drivers (Vin must be greater than Vf of the LEDs). Datasheet is at http://www.micro-bridge.com/data/CRpowtech/PT4115E.pdf