Per @Currawong, in most cases finding a readily audible difference between a standard CD-resolution file (16/44.1) and a commercially available high-resolution copy primarily tends to be a) down to them coming from different masters (most common) or b) because your’e bypassing/using different filtering in your DAC*.
There’s a c) case as well … which involves source material that has a lot of ultrasonic content played back on gear that doesn’t have the bandwidth to handle (or filter) it properly - and that can result in all sorts of undesirable audible artifacts/effects (and might not be good for the gear in question, either).
The only way to be sure that you’re not getting different masters is to start with a high-resolution file and then create lower resolution versions yourself, using high-quality re-sampling tools (e.g. iZotope or SoX) to produce the lower resolution copies from that common source file**. Any other test material is a bit too open to other factors to be trustworthy.
You can then use something like Foobar with the AB/X module to perform a controlled, blind, test and see where you wind up. It’ll even log the outcome for you. This tends to be quite illuminating and is worth trying for yourself!
I’ve performed this sort of test myself a number of times.
The vast majority of the time I cannot reliably discern any difference between the 16/44.1 down-sampled file and the original 24/192 (or higher) original. This is with short fragments of each track for each comparison iteration and a DAC that doesn’t oversample/filter differently based on bit-rate.
With a DAC that does oversample and/or have different filter behavior with changing input rates I can, in general, tell a difference, with reliability better than statistical chance. But I have to be focusing on what I’m hearing to a sufficient degree that I would never actually listen to music that way.
Finally, I’ve done longer tests, with entire albums processed this way, and the version I’m listening to selected at random (hardware random number generator), and typically found that I’m less “listening fatigued” at the end of my listening that I was with the lower-resolution content. But there are so many variables at work with this sort of comparison, that it’s a tenuous correlation at best.
Now, do I buy high-resolution content?
But only either a) when I have knowledge of/provenance for there being a material difference in the masters used for the high-resolution version and the commonly available CD or streamed version (e.g. the “Kind of Blue” reference @Currawong makes above) or b) it’s the only way to buy the album for download.
TL;DR; - I don’t doubt that using different sources for the different resolutions results in distinctly audible results - but the source resolution is probably not, by itself, the immediate cause. Where source resolution difference is the only variable on the input, audible differences are likely to be down to different/bypassed DAC filtering or other equipment artifacts.
*One way around this is to take the downsampled file, and then upsample it back to a level where your DAC’s filtering/upsampling is not in effect.
**This needs to be done properly and requires either quality tools with proper pre-sets, or you need to understand what you’re doing so you can apply appropriate dither when reducing bit-depth etc.