Ideally manufacturers should state the maximum voltage, and the maximum current the amp can provide, and state the output impedance.
To be useful though, you need a standard for how much distortion an amp can have before being deemed to be at its voltage or current limits.
You need an agreed figure for a fair comparison, otherwise you could rate a crappy amp at 1W with 10% THD (Total Harmonic Distortion). Sure, you get volume, but it will sound like crap.
Also, output impedance is important. Generally you want at least 10 times lower output impedance on the amp relative to the impedance of the headphones so you get flat frequency response, and sufficient damping to prevent distortion. This is a different issue to amp power. As well as enough power, you also need an output impedance that is low enough relative to the impedance of your headphones.
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So I have headphones with 32 ohms impedance and 112dB/mW sensitivity. They're nice and loud with Mackie interface, which has headphone out described as "max level 8mW into 600 ohms". They sound pretty weak even maxed out on Tascam, which has "18mW per channel into 32 ohms".
Sapphire 2i2 has headphone out described as 10 ohms, max level +10dBu. Can I guess from this how well would it work with phones like mine?
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The problem is incomplete specifications of the electrical performance of the amps.
You know how one amp performs into 600 ohms. You know how another performs into 32 ohms. But you don't know whether or not the one specified at 32 ohms is capable of producing extra voltage to keep the power up when connected to a 600 ohm load, or whether the one specified at 600 ohms can supply the extra current needed to keep the power up into a low impedance 32 ohm load.
Knowing that one amp can supply 8mW in to a 600 ohm load allows you to calculate the voltage the amp is applying to achieve that mW figure, and how many mA of current is flowing.
So, knowing the voltage, you can now calculate what the current and wattage of the amp would be into a 32 ohm load.
Bingo! Easy comparison, right? Of course it's not that simple. You don't actually know that the amp is really capable of supplying enough amps (same voltage as before, but only 32 ohms instead of 600, less resistance equals more current at the same voltage) to produce the wattage the calculation would suggest.
One solution would be to have everyone give specs for their amps at different loads, 16, 32, 64, 150, 300, 600 ohms. Then you could compare across a range.
A better solution would be if the maximum voltage and current capabilities of the amps were specified so that you could then calculate how many mW they could deliver into whatever the impedance of your headphones is.
In the case of the saphire, where it specifies +10dBu and 10 ohms output impedance, you can convert +10dBu in to volts, and if you know volts and the impedance of your headphones in ohms, you can now calculate amps and watts. But how much current is the amp capable of delivering? Can it produce it's full voltage with low impedance 32 ohm headphones without flowing too many amps and causing distortion, or can it only achieve that voltage figure into 600 ohm headphones where the impedance keeps the current flow lower?
At least it states the headphone output impedance at 10 ohms, unlike your other examples, allowing you to know based on the rough rule of 10 that your headphones should ideally be 100 ohms to have flat frequency response and good damping.
So, the first two tell you amp power, but at different impedance loads, and the last one tells you output impedance, and voltage, but doesn't specify what impedance the figure can be achieved at. Brilliant. And we're assuming that all of the specifications given are at an equal level of distortion, but we don't know that. Some may be more "optimistic" than others in the figures they produce.
Very hard to do a fair comparison without being given all the information, or actually measuring yourself the things they don't tell you.
The reasons for not stating all the necessary figures for a complete fair comparison include incompetence, laziness, lack of demand for info from the customer, a desire to hide just how average something is, or a mix of all those reasons.
It gets worse with consumer gear, like my Sound Blaster X-Fi Titanium Fatality Professional (yes, that is the real name of the card!), which only says it supports 300 ohm headphones, whatever that means.
Good reference for further reading, goes into more detail, and explains the math involved:
http://www.apexhifi.com/specs.html
and, a great video from an Audio Engineering Society presentation:
"Lies, Damn Lies, and Audio Gear Specs", Ethan Winer, Mike Rivers, Scott Dorsey, and David Moran.