You will absolutely be able to discern a difference between different headphones. Anyone who's not actually deaf could tell the difference between, just for example, a pair of mid-range Grados and a pair of mid-range Sennheisers. It's not subtle. The impossible question is "which is better"
To add to what someone said earlier in this thread - the basic thesis of ASR when it comes to headphones is that everything in your chain up to your headphones should strive to reproduce the original signal as accurately as possible, and then you should pick the headphones that *sound best to you*. It's really difficult to do objective measurements of headphones that are any use to anyone; the best we've got are these wacky head analogs which you stick the headphones on and do a frequency curve measurement which will be, at best, moderately accurate for any actual human head and pair of ears. This is complicated by the fact that a pair of headphones which produced a frequency curve that measured flat on a head simulator would sound really weird to human ears; humans prefer a distinctly non-flat curve, and different humans disagree on exactly how it should be, but there is a reference curve that's basically an average of a bunch of human preferences, which the measurements can be compared against. But your preferences might not match that average. And this doesn't tell you anything about, e.g., how detailed the headphones' reproduction is or how wide their soundstage, it only gives you a basic idea of their sonic...character. This is why there aren't any ASR headphone reviews like there are ASR speaker reviews; it's just not currently possible to do detailed measurements of headphones that tell you useful stuff like we can for speakers.
Oh, and we can measure isolation pretty well. That's about it.
Some people also like to try and find the 'ideal' frequency response curve for them and then use equalization to tweak the response of any given pair of headphones to match that curve and then compare the headphones against each other for other characteristics (like detail, comfort, isolation etc).
So really - the point where you get to the actual headphones is the point where the ASR philosophy more or less runs out, and you get down to your subjective preferences. There is no right answer to which pair of headphones is objectively the best. You can get a good idea of approximately what various types and brands of headphones sound like by reading around here and on head-fi (if you ignore the more overenthusastic woo merchants there), and that might help you narrow it down to some likely candidates that you'd be interesting in trying out, but at some point you're just gonna have to listen to a bunch - ideally in a quiet environment, from a good quality source, and with the ability to match levels and use eq if you like it - and pick which you like the most.
Factors other than sound quality can be just as important when it comes to picking headphones too. Comfort is vital; it doesn't matter if they sound like the voice of God if you can't stand having them on your head for more than five minutes straight. Depending on your environment, isolation and portability may also be very important.
Back in Ye Olde Times before the whole pandemic thing, there used to be big events you could go to and try lots of different headphones. Not so much now, unfortunately. If you have a relatively good budget and a high tolerance for dealing with people and shipping you can try quite a lot of headphones just by buying and selling second-hand. You might also check if you have a local hi-fi store; most used to be pretty snooty about headphones, but these days that's less common and good hi-fi stores often carry at least a few decent pairs.
Edit: to answer a few of your other questions - as fluffy said, impedance doesn't tell you anything about the quality of the headphones really. MOAR IMPEDANCE doesn't mean MOAR BETTER. Its only significant in the context of how much power you need to drive a given pair of headphones sufficiently (and how likely you are to hear noise). There are widely-admired headphones with all sorts of impedance levels.
I've never heard your headphones myself, but from what I've read they are a pretty well-respected mid-range pair. They're not trash by any means. So you probably shouldn't necessarily expect to buy something else and be blown away by a huge quality difference (though one thing we know about audiophilia is if you know you are listening to something expensive and you expect that to mean it's great, you'll probably perceive it as great...). Like just about anything else in audio, headphone quality is subject to diminishing returns; you will probably notice more difference going from $20 headphones to $200 than you would going from $200 to $2000 or $2000 to $20,000. You may happen to find something you greatly *prefer*. It's hard to predict.
On iTunes - AFAICT it seems consensus is that iTunes downloads and Apple Music streams are both 256kB/sec AAC format. Every human listening test I've ever seen has reported that humans can't really perceive a difference between that and the original uncompressed audio (this is the case for any decent codec - modern MP3 encoders, AAC, Vorbis, Opus - above 192kb/sec). The most recent test wikipedia lists -
https://en.wikipedia.org/wiki/Codec_listening_test#cite_note-1 - found no perceived difference between the original uncompressed signal and MP3 or AAC at 192kb/sec. So I would say yeah, that quality should certainly be fine.
