Im not a professional In this area by far. First off, a few questions I'd ask myself but don't know the answer to. I know that a speaker integrated amplifier with a headphone jack uses the power of amp for the speaker load but uses resistors to feed the jack. Let's say this amplifier could do all the things that make it a good amplifier such as good soundstage, low noise, control of the most minute dynamics and details, texture, realism. the amp was engineered to do that to a speaker. Do those traits carry over to the comparatively small load of the headphone? Not sure
Not all receivers, integrated amps, etc work this way. Some use separate circuits to drive the headphone output, usually an op-amp based design (but I've read of some implementing IC amps, like the popular TI TPA6120 family). The pre-amp/gain stages are usually preserved through though. It's usually a safe bet that if the amplifier is a switching design (e.g. Class D, Class H, Tripath, etc) the headphone amp is a separate circuit (because switching amplifiers generally don't like being run single-ended/bridged), and many DSP-enabled products use separate headphone output circuits as well (to better integrate with the DSP side).
To the question about sound: it will be somewhat different (vs with speakers) no matter what. In the case of the main amplifier driving a resistor network, you usually have a large output impedance, which can interact with reactive loads and have an impact on frequency response, plus the whole "synergy and pairing" thing of that amplifier + the headphones (and remember headphones are a lot more sensitive to noise floor and channel tracking). If it's a separate circuit it can be a whole 'nother animal from the main amps. That said, IME hi-fi amplifiers with headphone outs have never sounded "bad" - sure some of them are better than others, but usually they're always at least decent sounding. For example my DSP-A1 has an op-amp circuit for the headphone output, and while its certainly not the best sounding amplifier I've ever heard, it's more than good enough sounding with anything I've plugged into it. By contrast, I've got an old Kenwood that runs something like 650R off the main amps, and while its a very clean and neutral amp into speakers, into most headphones its warmer than a sweater fresh out of the dryer.
Now here's what I have gathered as far as the power differences. Once again, not a professional in this area.
Maybe someone will chime in a help if I'm missing something here,
a speaker amp only needs to handle fluctuation of impedance in an area from on average 4ohm to 8 ohm. There is a lot of current needed in this area but the voltage stays the same and is low. This is fine for a planar headphone as there is no impedance swing varying through frequencies. The integrated speaker amp will simply use a series of resistors to restrict the power it has for speakers which is current. A low impedance planar needs current so this is good.
Firstly, speakers usually have significantly broader impedance fluctuations than "4 to 8 ohms" - that's just nominal impedance. There's also generally more of them than you'll find on a headphone (due to the crossover and multiple driver/box resonances). The voltage output of a conventional speaker amplifier is also usually an order of magnitude (or greater) higher than what most any headphone will survive (or any headphone amplifier will provide) - 20Vrms is not an uncommon output (and voltage does not "stay the same" - you adjust it up/down as you adjust volume up/down - technically the amplifier is providing X voltage gain and you're varying what's going into it, but the output voltage is what varies up and down, not the output current (which is the result of impedance + output voltage interaction (per Ohm's Law) and this is where/how you get some speakers popping amplifiers by demanding more current than the amplifier can service). Current delivery is orders of magnitude higher than what any headphone will need (or survive). The resistor network is generally trying to bring the output down to around 2-5Vrms (the IEC spec is 5Vrms at 120R, but for a lot of amplifiers 120R is not enough to get the level that low, so its not uncommon to see more 5Vrms at 400-600R).
Due to the resistor output network, the output power is pretty stable into a wide range of loads, and distortion is generally minimized (this is why the IEC specifies things the way it does). However that high output impedance will interact with reactive loads (this doesn't mean a low output impedance is "better" or "worse" - its just a different kind of interaction).
If you want to see an example of that plotted:
(What am I looking at? output power vs load impedance from an amplifier that provides a 120ohm output - this is an opamp driven amplifier)
Distortion is well managed too:
Power output is pretty consistent across the range of loads, and distortion says pretty low. On lower output impedance amplifiers it isn't uncommon to see much bigger numbers into low impedance loads, and power output to drop off more significantly into higher impedance loads.
You can read more about the IEC's standard here:
http://www.epanorama.net/circuits/headphone_attenuator.html (the actual standard is described in an IEC standards book that is behind a paywall)
You're probably right that even a resistor-driven output will not be sufficient for a very hard to drive pair of headphones (e.g. K1000, HE-6, etc) which is where balanced drive via speaker taps may be worth consideration - the jack on the front may not have enough oomph, but the taps on the back probably have more than any ten cans should ever need.
However, some dynamic headphones need more voltage such as a 600ohm beyerdynamic t1. A speaker amp was not designed for this type of voltage and it's swings. Now I know that the voltage output is a constant and im pretty sure the speaker amp can come up with the power to drive them to listening levels given that they spec it to release a certain amount but I don't think it's ideal.
The T1's require a fraction of a volt to reach fairly loud levels - the output of a typical speaker amplifier is still more than enough to cook them off pretty quickly. Hooked into the output through a resistor network should be no problem, because again the performance will be pretty consistent as a result of that design; running from a dedicated circuit may or may not work out well based on whatever that circuit can do in terms of voltage supply.
