I'll chime in and give my two cents. In general, the myth that integrated amps have bad sounding headphone outputs is pure ********, sorry, but that is my verdict after trying out a lot of them. And people who say so in most cases have no experience and haven't actually tried out the amps for themselves. The only issue that such headphone outputs have is high output impedance, so using low impedance headphones, especially if they don't have flat impedance curves, may change sound slightly. We're talking about 1-2 db changes in frequency response, usually in the bass region, and slight lack of tightness, which is NOT always bad, as it can make some bass light headphones actually sound better, and a lot of professional low impedance headphones (that are used as listening headphones too) are tuned to work with higher impedance outputs on studio mixers, consoles and interfaces. But, if you use high impedance headphones, 250 Ohm Beyers and above, or 300 Ohm Sennheisers, you don't have to worry at all. Some low impedance cans such as AKG's don't give a damn about the output impedance either, since they don't seem to change much at all. All in all, yes, they're not ideal for low impedance headphones, but neither are OTL headphone amps, and you don't see people saying that all OTL headphone amps sound bad because they don't sound perfect with low impedance cans.
Anyway...I had these very same doubts until a about 2 years ago, when I actually went out to several hi-fi shops with my headphones (DT880 600 ohm at the time) and tested about 30 different integrated amplifiers and receivers ranging from entry level to high end. That was 2 years ago, and even though I have written notes somewhere, I won't go into detail about how each of the amps sounded. I'll just talk in general. None of them, I repeat, NONE of them, had bad headphone outputs. None of them had any noise with DT880, none of them lacked power (could hardly turn volume past 50% on most of them), none of them had problems with channel balance, none of them had problems with keeping the frequency response of the DT880's flat and keeping all of their characteristic sound qualities. They sounded different, integrated amplifiers by rule sounding better than receivers, but in general, all of them made the DT880's sound exactly as DT880's sound, with slight variations in quality when going from entry level NAD's or CA's to stuff like Naim.
I did a direct comparison at the time, it was between an Onkyo A-5VL integrated amplifier with an integrated dual mono 24/192 Burr Brown DAC (one for each channel), which I chose to buy because I needed an all-in-one amp for my second speaker setup, that amp was a 450€ integrated amplifier back then, and I compared it directly to Asus Essence One, Cambridge Audio Dacmagic Plus, Teac UD-H01, Nuforce HDP, P Little Dot MKV and Musical Fidelity V-CAN2, all fed by the same Marantz SACD player, think it was a 8003 or 8004, don't hold my word for it. All of those DAC/headamps were priced at or above the price of the Onkyo amplifier, MF V-CAN was about 300€ as a standalone little headamp. I used only DT880's to compare directly, so keep that in mind.
In which ways was Onkyo better than all those?
1) Considerably more power, heaps of power and headroom. While each of those dedicated head amps struggled to make the DT880's sing even when turned to full volume, and some of them clearly distorted, Onkyo played at the same volume, with unquestionable control and authority at under 30% at the volume pot.
2) Onkyo had no channel imbalance whatsoever at any volume knob position, all of the above had those problems except the Dac Magic which has a digital volume pot, but as a device it sounded so bad it doesn't really help it.
3) Onkyo had no hiss present at any volume, Dac Magic, MF, LD and Nuforce had.
4) Onkyo had on-board EQ controls that actually work, and don't just make the bass bloated and muddy, or highs sharp and piercing. I usually don't care about EQ, but this one actually works, and works damn well, since it does exactly what you want it to, without messing with the rest of the sound in any audible way.
5) Onkyo had more authority in the sound than any of them. I can explain that most easily if I say that headphones sounded more dynamic, lively and sound had more authority and PRAT. Simply put, any of the above sounded flat and boring, with an exception of Asus Essence One and LD Mk5.
6) I distinctly remember that Onkyo had a more spacious sounding soundstage, and projected the sound more forward.
7) In terms of resolution, detail, clarity, extension in both ways, tonal qualities, and all other audiophile terms, Onkyo was as good or better, with an exception of Asus Essence One, which did sound a bit more detailed and smoother, but had limited power, at least that's what my notes say.
Long story short, I walked out of that store buying the Onkyo, instead of a integrated amp + DAC/headamp as I planned before entering, since the Onkyo did all three tasks on it's own better than any of the others. And it wasn't even the best sounding integrated amp that I've tested, not by a long shot.
Now, I have several receivers and integrated amps, as well as several DAC's and headphone amps, and a lot of more headphones than I had back then. However..... T1's, HD650's, DT880's. DT990's, DT770's still sound good enough to me out of any of those. T1's plugged into the Onkyo amp sound 90% as good, with no obvious faults, and isolated on it's own without A-B testing, just as fun and engaging as when plugged into a Musical Fidelity M1HPAP (which costs twice as much as the Onkyo in my country) and a M1DAC (almost as pricy as the amp). On top of that, the best I've ever heard out of T1's was not out of OTL's, or higher end headphone amps than what I have, it was out of a high end Naim integrated amplifier.
