The sampling rate isn't normally going to "change" the sound, but rather help in the realm of accuracy of the original audio. If you've ever been through Calculus classes (Limits and Integrals), you can start to really dig how sampling and bit-depth come into play. In all reality, 44.1Khz might be good enough of a sampling rate for human ears, which is why CD Audio was set to that, and any frequencies above 20Khz in the audio were essentially filtered out in your CD players.
For most ears, 44.1Khz is plenty good. However, Audiophiles will fight to the bitter end that you can actually hear/perceive frequencies way beyond 20Khz, which aren't specifically interpreted by your ears and brain as sound, but cause your brain to release chemicals that help "sweeten" the audio so that because of the super-sonic frequencies only birds can hear make cymbal hits and such sound sweeter and less fatiguing to your ears.
I don't know if I'd immediately subscribe to this, but just as an EQ can bring up frequencies around the center band of a boost, so, the accuracy of the top-end sampling rate can (in theory) more accurately allow you to record even higher "audible" frequencies, whether anyone cares or not.
Now, 24-bit vs. 16-bit is audibly different. Dynamic range is more apparent in 24-bit vs. 16-bit especially when it comes to loud frequencies and super quiet. Many claim more 3D to their audio. I just feel it's less claustrophobic and more "open".