Vinyl through a tube amp sounds "fuller" and "richer" because it is injecting a type of interference that the human ear finds pleasing. In other words, it may "sound better," but it isn't technically an accurate reproduction of the sound.
The way digital sound works is by sampling at a rate far greater than the human ear can hear. The human ear can discern sounds greater than 20KHz in frequency, and if we sample at least twice that often, we won't be able to tell the difference between analog and digital sound. This is why a good MP3 is sampled at a rate between 96 times/second and 128 times/second (any higher than that is a waste of CPU time and hard drive space).
The main advantage of digital sound is that it is recorded digitally, and digital recorders make exact copies each and every time. If you tape a record to cassette, and then that cassette to another, and the second cassette to a third, after a while the last cassette is going to sound terrible (and over time, it will degrade). Digital copies are identical no matter how often they are copied, and CDs last for a very long time without fading. Commercial ones do anyway - recordable homemade ones may fade after a while, but I don't remember how long it takes.