There’s no analogue audio over Lightning, so if the 30-pin adapter is disabling volume level on the phone, it’s just picking a fixed gain for its internal DAC—perhaps because the DAC is only good within a certain gain range. The Apple USB-C to 3.5mm adapters are widely regarded as having excellent DACs irrespective of their size and price. I’m not as familiar with the reputation of the Lightning to 3.5mm adapters, but I would consider the ability to configure the DAC volume an indicator of superior quality DAC compared to the 30-pin adapter.

The Lightning-3.5mm adapter has a quite good DAC for its size, I remember seeing a teardown article from when it was first launched, quite impressive engineering going on in a such a small piece of electronics.

I'm pretty sure it's the same DAC since the signal is digital whether over Lightning or over USB-C until it hits the DAC.

They earned their reputation when new phones came packaged with the adapter for the first few generations (circa iPhone 7/8?) after the 3.5 mm jack was removed.

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