is underpowered amp underpowered? yes. ^_^ glad I could help.
there are a few points to address here:
-subjective reports, are mainly the kind to associate 2 things for no reason. the 2 amps will have about 5 hundred significant differences in design and specs, but the guy will go "amp B has a lot more power, I've seen that on the box, that's why I feel like the bass is better". and the 499 other potential reasons? well nobody ain't got time for them.
you never know if 20 people will tell the same thing because that's how it is. or if they all read some review from that famous dude and now they regurgitate something wrong or half understood. or simply if they say the same thing because the intuitive conclusion tends to lead there(right or not). like with, more bass requires more power. out of context it's obviously right so why not take that and use it to argue anything? of course people will think that way. so because I never know what to think, I chose to apply a massive amount of skepticism 9000 over any subjective claim.
-specs:
for headphone and for amps, specs are typically given for what's happening at 1Khz. so of course we have no idea of what is going on elsewhere. the point of those specs is to be able to make an approximation of the needs and behaviors. and for that job it works just fine.
the hd650 is given as about 300ohm, but the impedance goes a good deal higher around 100hz. we don't have such information in the default specs. so different amp impedances will result in slightly different levels of boost at 100hz. so the amp design and other specs become at least as relevant as power. some amps with have zero something impedance while others will have 30ohm or more. but just like for the headphone, those values are usually for 1Khz, some amp designs will show impedance variation throughout frequencies.
another thing is that not only the power specs were given at 1khz, but also into a 300ohm load when we look at amps for the hd650. so at 100hz the load isn't 300ohm anymore and we would need a different measurement anyway even if we didn't have the 1khz vs 100hz issue.
but most people giving subjective feedback don't even have a clue that those stuff exist, so of course they won't consider what they don't know. mooooaaar power becomes the likely scapegoat. you can never be wrong when you ask for more of something right... but that too is false.
-enough power, then more:
clearly, just measuring 2 frequencies like in your link and drawing conclusions from there is faulty. headphones don't have a flat frequency response, the bass rolls off at 80dB and it still rolls off at 90dB just adding power to the amp will not magically make the bass louder but somehow keep the midrange at 90dB. it makes no sense to think that way, be it with a functional or dysfunctional system.
sure enough if we are dealing with an underpowered amp, then many things can go wrong, but most likely we'll see 2 situations. we can't get the sound at the loudness we desire, or we'll start getting very significant distortions. an amplifier trying to send more than it can usually doesn't take it too well. if the only consequence is a little anemic bass, we're in one hell of a lucky result.
in the end we have enough power or we don't, more than enough doesn't send anything more to the headphone(unless we go louder). maybe a relevant data would be to measure distortions at different places, and sure enough we could do with a few more measurements when we purchase an amplifier. but that has nothing to do with subjective feedback.
so for my conclusion, I'm tempted to say that power arguments should come from actual measurements(duhhh!), not random subjective impressions about the low end on 2 different headphones. or some dude who has 2 completely different amps but somehow can only think about power. what else could possibly be different between 2 different amps? ^_^ people don't know how to solve a case. if audiophiles were playing Cluedo (Clue), most would go "it's colonel Mustard with the rope in the kitchen" after the second turn. then they would get offended when you dare point out that they're wrong and didn't have the means to draw that conclusion just yet anyway.
