A pot in a box will outperform an active preamp in some ways like transient speed and noise because there's only the pot in the signal path. But there is a cost. A well designed active preamp can be as clear as a pot and add the buffer which is needed in most systems. Voltage amplification is usually not needed in the simple systems most of us use today, that's why passives keep popping up. But they don't take over the world because after the transient clarity buzz wears off, you realize you miss the current buffer powering the wires and input stage adequately. You lose density and wonder, "Where's the beef?"
The autoformer is quieter than the pot because there are no resistors. You will have some harmonic distortion from magnetic induction but it is 3rd order and most people consider that harmless or even desirable.
The LDR is a resistor, but quieter and more transparent than the pot. It has virtually no harmonic distortion.
There are no temporary or sliding connections with LDR, all signal connections are soldered. Temporary connections like a pot slider or switch add noise and raise impedance. A pot has sliding plastic element, so music goes through a piece of metallized plastic. With the autoformer you switch between one winding and another to change volume level, so you need a switch. There are very good switches in the world, but they still add noise and impedance, and need to be cleaned, cost a lot, etc. But autoformer is a lot better than a pot.
I think the Axiom uses an Alps pot for the variable element, and uses a few passive resistors to improve the circuit. For $149 there can't be much in there.