interresting subject.
I used to own sony XBA-3 and XBA-40 IEM's and now own sony XBA-300's along with Westone UMP PRO 30's.
I used the XBA-3's and 40's a long time on my smartphone (Sony Z1 and Z5) and was quite happy with the SQ. I then tried them with a portable amp in the middle during a visit in Japan and it was a revelation to me as the music seemed much more dynamic, lively etc etc to the point I had to buy an amp on the spot (a sound blaster E1 replaced by FiiO E11K later)
my subjective experience tells me these four BA iem's need amps to perform best, and the impedance curves seem to hint in that direction, but was it all illusions?
I'll take a different stand on this, my buddies might not be familiar with those IEMs or most IEMs in general.
the impedance curves alone are more than enough to explain some audible differences from different sources. if you had the bad luck of going from some high impedance output on one source to one around 1ohm or less on another, it wasn't in your head. nobody would have dared to say they sounded the same after trying them. I only played with the xba3 and 4 at the time but they were such a perfect case study of what not to do if you seek something stable.
those IEMs went as low as 10ohm if I remember correctly, so while not dangerously low yet, when a device writes from 16 to 300ohm in the specs, they could put that 16ohm value because everybody did. or because their design was really not good with lower impedance loads. there was a fairly famous case of a samsung phone supposed to have good audio stuff, low impedance etc, some time back where the phone would start distorting like mad into several low impedance IEMs when the user was pushing the volume level a little. the IEMs were simply outside of the usable range and samsung failed to consider the situation of crazy low impedance IEMs.
but I would strongly advise against taking that experience with sony IEMs or any multidriver IEM reaching very low impedance somewhere, and use it to think that it shows the need for a portable amp in general. it really doesn't. to make a point, the irony at the time was that sony DAPs were around 3 to 5ohm(lame), and the PHA1 was something like 8 or 10ohm I think. we even came to a point where some gears got a list of suggested pairing and half the sony models weren't in the list made by sony ^_^. it was like they had made those IEMs and amp to troll themselves.
a simple rule of thumb for stability and low encounters of troubles: avoid gears with weird specs! too low impedance, crazy impedance curve, crazy high sensitivity, any extreme is a chance for trouble with at least some sources. that said most TOTL IEMs are such troublemakers. stuff with a gazillion drivers and 80crossovers with super extreme sensitivity and impedance reaching very low. so my rule of thumb would be to avoid all of those like a plague, which can seem like a strange advice to audiophiles but I stand by it ^_^. stability and versatility are unlikely to be found in the most extreme specs.(applies to politic! viewed on TV!).
I like to use my sony DAP( A15) with crappy amp section, because it's small and I enjoy the UI, but with it I use a limited list of IEMs. with my pair of RE400 (about flat impedance at close to 35ohm), I can really use about any source I like and they sound very fine and pretty much the same to me. even with my se215(around 18ohm but still flat impedance), everything is fine on all my sources and I can hardly tell them apart.
but I have a few IEMs where I can basically tell you which of the sources I own is being used by ear. they will create or exacerbate differences. when it's audible background noise or distortions so bad into a low impedance load that it's audible, the better source is a simple matter. you need one with lower noise floor or one that doesn't piss it's electric pants when the current flow gets a little high. but when the result is simply a signature change, the notion of better source can be a matter of personal taste. it's not really that one is better contrary to all you'll read in the reviews, but that with a given source, the guy likes the signature more and that's most likely all there is to it. maybe you would agree, maybe not. and the low impedance amp that measures so good might not be your favorite pairing. many people really loved their sony PHA1.
some IEMs/headphones will invite stability. others won't. I tend to think that stability is a sign of a product well done, but elitists just love it when something needs special care. to each their own.