Is there a noticeable difference between .mp3 and .wav sound quality?

just wondering if people can actually tell the audio difference between .mp3 files and .wav files. I have a deadmau5 track called "bye friend" as a .wav file and is 56mb for about 6 mins of sound. Much higher file sizes, but is it worth it? Also, is it true that .wav files produce better sound at high volumes?