I think redbook CD format specifies the dynamic range for the 16 bit format and is fairl y standardized as a result.
Not sure this is the case with other newer hi rez digital formats?
More bits enables more dynamic range and more detail together. How this happens might be highly variable in lieu of a standard.
In any case, for hi rez digital sources, I suspect a difference associated mainly with the high frequencies can be heard if done right, but that may be a big if at this juncture still.
To hear the most possible, you definitely want very good, younger ears, speakers that can handle dynamics and transients well and also have very good detail assuming the production is done well and the DAC not only reads the format but is able to output analog of similar resolution and quality.
At this still emerging stage of hi rez digital audio, I doubt it is a safe bet that hi rez source material and playback gear meets these requirements well in general, although I am sure there is some reference type recordings and better gear that do.
The first place I would listen for the difference is in well recorded massed bowed strings in orchestral music. Use a good modern RTR reference recording as a reference standard. Even older trained ears should hear a noticeable difference if the digital is not extremely well done.
I have had the opportunity to listen to RTR, vinyl, and good redbook CD recordings on a very well done dealer system using mbl 111e speakers. The difference from RTR to redbook CD was pronounced but you might not notice the limitations of the redbook CD unless compared to the RTR or even good vinyl on a similarly good system.
The SOTA wide and deep soundstage in this optimized and very resolving mbl setup provided exactly the venue size and 3 dimensonal sound quality needed to be able to hear these kinds of differences clearly. Quite an eye (ear?) opener!