The Magni II specs (130mW : 600 ohms) calculate out to appropriately 8.83V output. The whopping 1.8W : 16 ohms calculates out to a current limit of about 335mA, where the the Pulse output of 3.025W : 16 ohms is about 434mA. The Pulse provides a solid power doubling for every load impedance halving down to 16 ohms where the Magni II starts power limiting around 100 ohms load.
As an aside, 130mW into 600 ohms is only about 2.5dB more than 81.66mW into that same 600 ohms. This is only a little louder, and nowhere near the twice as loud as some think it should be.
As I said, high impedance headphones might be better served by a medium power speaker amp that can deliver the higher voltage required to drive them to a high power level. For example, an 80 watt into 8 ohm power amp would provide about 25.3V and be able to drive 600 ohm headphones to about 1.066W. Also, high impedance headphones are very well served by tube amps and are well suited to the Output Transformerless variety, as these naturally provide high output voltage but are limited in output current.
The ability of the Pulse to maintain its output voltage of 7V down to a 16 ohm load actually ranks it as rather sturdy. The ability to deliver the higher current to achieve this also means that it will have more control authority over all headphones than a more current limited amp such as the Magni.
If you need more power for high impedance headphones then you will need a specialized amp designed for this far end of the spectrum load. While there are some very fine headphones that have this (nowadays) unusually high impedance, the vast majority of headphones are in the range of 16 to 50 ohms or so. Specialty headphones often deserve and require specialty equipment to get the most out of them.
J.P.