I imagine it would be a tough comparison between pumice and the other two since pumice can have a highly variable density depending on grain size. If you're talking about the density of a single rock of pumice (which is also variable) you would also have to consider that the larger the rock is, the less surface area it has available for exchanging cations.
That said, ADA's powersand (at least according to Tom Barr's analysis) is essentially pumice mixed with peat moss. ADA Clear Super and Tourmaline BC are activated carbon and bamboo charcoal, respectively. So if you took a mixture of pumice, peat, and activated carbon/charcoal and charged it with either dry ferts or osmocote, you would theoretically have created a bootleg version of the ADA substrate system which by all accounts is great for growing plants. ADA only recommends a thin layer of this substrate beneath aquasoil.
Back to your original question of how much dirt to use -- Cory from Aquarium Co-op suggests just a small amount (maybe 1 cm) of dirt below a thick cap. Having recently had a thick layer of dirt capped by aquasoil, I would agree with him. Once the plants' roots reach the dirt layer, uprooting gets super messy. If you're using CO2 you're going to need to uproot plants eventually. That dirted tank I had grew plants super well, but it was also the version of tanks that was best at growing algae due to all the dirt I was constantly bringing into the water column.
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