In a nutshell: nullc, rahimnathwani, zamadatix and vor_ know their shit, and geraldmcboing and PaulDavis are technicially correct but talking past each other. speak_on and TheOtherHobbes are confidently wrong.
And also: 44.1 kHz captures the entire human audible spectrum with room to spare, and 16-bit already goes beyond anything useful for listening. The higher resolution / sample size format is useful for production or archival purposes only.
The two main reasons why you hear a difference between the two formats: (1) it's likely a different master, (2) tiny gain differences in the signal (salesmen use this trick, but it's also easy to do it by mistake).