I understand the difference in principle, but not in experience. If you were to be sitting in the library and you would want to drown out the droning sound of a fan and an A/C unit, which one would you use ? Would you say that AKG or PSB M4U2 would do the job as well as Bose to drown out in this specific situation ?
ANC will work on frequencies below around 1khz, everything over that is going to be passively attenuated (and in that regard, the AE2 and QC15 are about evenly matched (that is to say, good)). The ANC is very good at removing the noise from air handling, jet engines, computer fans, and that sort of thing, but it won't do a whole lot to remove instantaneous noises (like say, if someone were to shatter glass, or loud talking/yelling). The QC15 will still "muffle" everything (just because they're decently isolating as sealed headphones), but if your goal is to knock-down people talking or other noise along those lines, the AE2 will probably do about as well (as will a number of other closed headphones). Remember, the original design goal here was to remove engine noise for aircraft passengers/pilots.
I haven't heard the PSB or the specific AKG you've mentioned, but from other ANC headphones I've heard (Klipsch, Parrot, Beats, Sennheiser, etc), the Bose are in another category in terms of how well they work. Tyll's measurements of the PSB show them being considerably behind the Bose in terms of isolation performance (roughly 10 dB difference broadband); no idea how they sound though.
I want to get the best for the price. I am willing to trade off a little in terms of features. Bose QC15 is the best - There is no disputing that - concerning noise cancellation. But, what about the others. AKG for instance. I have seen a reviewer saying that the ANC is as good as bose QC3. And the sound is way more superior. So I regard that as a fair trade-off. i.e Get the second-best ANC + great sound quality. See what I mean ?
Well, here's the thing (and this is the point I've tried to make twice now), there is no linear, 1-10, "sound quality" variable (despite what a lot of people insist/want). There's only "better" or "worse" for you and your situation - speaking just to isolation, the QC15 are going to be about as good as you're going to get in a full-size headphone at any price. And that's basically what you asked. Speaking to sound quality preference, well, that's a personal question. What do you like? What do you dislike? This preference discussion becomes more relevant when you say "the sound is way more superior" or whatever else, it's about as informative as me telling you the square root of Neptune is tomato paste times poodle. It really doesn't tell you anything.
Also how would say QC3 fairs againsts QC15 in terms of noise cancellation ?
No idea - I've never even laid hands on a QC3, nor have I ever found a decent review of the QC3. In general, pillow-pad headphones are very hit or miss when it comes to their sound, and I'm guessing the QC3 are no exception to that.
Obobskivich, I really don't think they're competent at their price point. Based on the sound alone, I'd say they're worth maybe $50 at best. They're extremely muddy and distorted sounding to me. True, many headphones in that price range call for amplification, but even those headphones unamplified sound far better than the Bose ones do. The Beyer DT770's cost about half as much, are very comfortable for long periods of time (OP said he doesn't want his ears to get sweaty, which the Bose will do), have decent passive isolation, and mop the floor with the Bose headphones in terms of sound quality. Anupam also said he can buy an amp, so he could get a Fiio E12 and still come in far under budget.
I think we're just going to have to agree to disagree and chalk it up a difference of opinion - to me, Beyers are just clash-trash clap-trap. And if you knew anything about me, you'd know I don't play The Price is Right unless Bob Barker is hosting.
I agree with your point on the ANC (as I'm guessing you've already deduced) - it's good for certain applications, but not for others. Unfortunately there seems to be an unrealistic expectation/understanding (I blame Beats, but that's another discussion) that ANC will just remove all noise from all situations and produce "quiet" - when in reality it can only act upon certain kinds of noise. There are high-isolation headphones (Vic Firth makes a few pairs, so does Howard Leight), which will absolutely get you to that "quiet" point, but they generally sound pretty terrible (usually they're thin, boxy, and blanketed), and aren't very comfortable (but they aren't meant to be high fidelity products, they're meant to protect your ears and provide you with audio for communications or monitoring).
I wish I knew how to make the high-pitch ringing go ... 