CDs and vinyl LPs both have their respective strengths, and their respective weaknesses, which makes comparison somewhat of an apples and oranges comparison.
To make matters worse, commercial recordings, both analog and digital, have not always been of the best quality possible for their respective formats. A good example is Aerosmith's first album. If you listen to the vinyl of this, you can hear the hiss of the original master tape.
You should not be able to hear this hiss. At the 28 inches per second transport speed of the high quality, professional recording equipment of the time, any hiss would only contain frequencies well above the range of human hearing. If your dog were an audiophile it might bother him, but human ears reach, at most, 20khz. Most ears top out at well under 18khz.
However, if you have an old tape that has been extensively reused, you can indeed get audible hiss at these speeds. Overuse of dubbing will also increase noise in an analog recording, because once the noise is there, there is no way to remove it without also removing signal.
A third posibility is that Aerosmith could have made a "demo" tape at 14 ips or even 7, which the record company could have "produced" the finished album from.
Their second album contained no such hiss. But someone who had only heard CDs before, listening to Aerosmith's first album through headpones or good speakers, might conclude that noise was a terrible problem in analog and digital is always better.
Noise is analog's biggest weakness. Its other great weakness is that when you make a copy, the copy degrades. With a digital recording, all you are copying is an incredibly large number from one computer to another. Each copy is identical to the copy it was copied from.
With analog, each copy of a recording is a completely new recording. It cannot have equal frequency response, nor can it have less noise, or a wider dynamic range.
The analog media most people are accustomed to are the vinyl LP, cassette, and there are actually a few eight tracks still around. Eight track should have been superior to cassette, as it has twice the transport speed of cassette.
But it wasn't. Play a cassette and an eight track side by side, and the cassette consistantly outperformed the eight track. Why? Because the record companies saw the eight track as for cars with their abysmal acoustics (much worse in the 70s than with modern cars), and the cassette for homes, with their superior acoustics and (at the time) superior speakers.
Home made eight tracks recorded from LPs often were superior to the factory produced cassettes. But with non-home made tapes, cassette ruled, despite what should have been its technical shortcomings.
Pink Floyd "fired" their first record label because the master to their third album sounded "muddy," presumably because the tape heads either had not been properly cleaned, were worn, or the studio's acoustics sucked. Certainly Dark Side of the Moon had none of these problems, and went on to be the best selling album of all time, still on the charts thirty years later!
Analog suffers greatly from lack of cash. With a digital recording, even the cheapest CD player sounds good if played through good speakers. Not so with analog. With analog, the more you pay for a piece of equipment, the better it will sound. A cheap Radio Shack turntable will have "rumble"- the rumbling of the platter's bearings. It won't sound clear, and likely will have the bass attenuated to minimize the rumble, and the treble attenuated because it will sound tinny without the bass. Likewise, a cheap cassette player may have a very severely limited frequency response and still have an annoyingly audible hiss.
In music, "dynamics" is the variation in sound volume. Probably the one piece of music with the most profound dynamics is the 1812 Overture, simply because it uses cannon as a musical instrument. Few stereos are powerful enough to reproduce the cannon accurately, and no recording medium yet devised has the dynamic range to do this piece justice. Not that it matters- if you fired a real cannon in your living room, you would not hear anything at all for quite some time. Certainly you would not hear another note of the performance, bacause of the ringing in your ears.
The fact is, even cassettes have a wide enough dynamic range that the entire range is seldom (if ever) used in a musical recording. CDs have a superior dynamic range than LPs, which have a better dynamic range than cassettes. Even so, many CDs that were remastered from analog media (like the aformentioned Beatles album) have even less dynamics than their original LP! A good example of this is Led Zepplin's Presence.
Why should this be? Presumably because you can always turn it up, or even buy a more powerful amplifier. Some studios use only half of the CDs dynamic range, or even less. I bought a CD of classical music that was so wimpy I decided to make a "corrected" copy, ripping to .wav and normalizing it.
It was so aliased I threw it away, and contented myself with the weak original. Until I could buy a better performance (and recording) of the piece (Swan Lake, IIRC).
Just beccause one technology is inherently superior to another in one way or another does not in fact ensure that an application of that technology is superior.
The CD's format has two distinct disadvantages to both cassette and LP, caused by the same shortcoming- its sample rate and to a lesser extent, using only two bytes of resolution per sample.
This was forced by the technology of the time when digital recording was first starting. In the late 1970s when digital recording was born, 44 k samples per second was the best the equipment of the time could do. It was deemed "good enough," since the labels "golden ears" (humans with hearing well above average) didn't hear any noise and the sound of aliasing was something they had never encountered. They knew what hiss sounded like. They knew what a "muddy" recording sounded like. They knew what harmonic distortion sounded like. They knew what clipping sounded like. But aliasing was new, and they didn't hear it- because they could not possibly listen for it, as they listened for the above mentioned distortions they knew.
At a CD's 44 ksps sample rate, the very highest frequency it can reproduce at all is 22 khz. This is well above human hearing- but here, the model fails. Because its 22 khz frequency response is not an undistorted response.
With a 28 ips analog reel to reel, you can record a dog whistle with no distortion, and transfer it to LP, also with no distortion. In fact, these two technologies had become so good, with a frequency response so high, that they introduced "quadrphonics," or four channel stereo, in the early 1970s. It was a complete flop, since a $300 stereo sounded much better than a $300 quadrophonics system. You needed four of everything for quadrophonics, as opposed to two with stereo.
So, with only two sides of a groove in a record, how did they get four channels?
In a stereo record, the up and down motions of the stylis (needle) translate into both channels of the stereo signal. This way an older, monophonic record player could still play a stereo record without losing half the signal.
The right channel comes from the side to side motions of the needle. To get the left channel, the right channel is mixed out of phase with the combined channels, cancelling itself out in that signal, which becomes the left channel.
With quadrophonics, the rear two channels were modulated with a 44khz tone and mixed with the other two signals, then demodulated at the turntable. This illustration is important to highlight the incredible frequency response of the 28 ips reel to reel and the vinyl record. These incredible frequency responses are completely undistorted. Were the supersonic carrier and the signal it carried distorted, when demodulated it would have sounded terrible. In fact, had you enough cash to afford a good quadrophonic setup, you would not have heard any difference in quality between the front channels and the rear channels.
By contrast, at high frequencies, CDs do very badly indeed. The best cassettes were capable of reaching 18khz without distortion, and even modest, affordable cassette players reached 16khz. If you had both the vinyl and the cassette (many people bought two copies of a piece, an LP for home and a cassette or 8-track for the car) you could hear the difference in the responses of cassette and vinyl. They were very striking, and it didn't take an audiophile to hear them.
By contrast, a CD doesn't even hit 15khz without horrible distortion. A little third grade math using graph paper explains why. A 15khz tone recorded on a CD has only three samples per cycle!
A sine wave curves up, then descends past the zero point, then curves back up to the zero point where it starts a new wave. A square wave goes straight up vertically, shoots horizontally, then straight down to its negative, where it repeats in reverse. A sawtooth wave goes up at a 45 degree angle, then back down at a 45 degree angle to the negative crest, then back up to the zero point.
A guitar player's "fuzz box" converts the complex sine waves coming out of his instrument into a sawtooth wave, or a square wave. Most fuzz boxes have a switch to select sawtooth or square.
At only three samples per crest, there is no difference whatever between a sine wave, a sawtooth wave, or a square wave. And a sine wave that sounds identical to a sawtoth wave is horribly distorted.
And here is where our action adventure nerd protagonist was right. A CD that was produced from an analog master will have the worst of both worlds, both analog media's more limited dynamic range and its noise, coupled by the CD's abysmal frequency response.
When CDs first came out, LPs had been mastered from digital tape for a few years. These CDs must be superior to their LP bretheren, since these LPs will have all the noise of analog, with none of LP's superior frequency response.
But remastered CDs made from an analog master is a completely different thing. Like the early digitally mastered LPs, they are the worst of both worlds.
But six hundred bucks difference??? Well, maybe if you are a chemist for the FBI, or your name is Larry Elison. Personally, the two dollar LPs I find in the used record shops are good enough for me.
As to the aformentioned Presence CD, it lacks presence. The original LP was recorded at the cutting edge, pushing the limits of the recording technology of the time - and analog recording was at its zenith. When it was remastered for CD, the highest frequency harmonics had to be attenuated to remove the aliasing. This made the bass sound too dynamic, so it was attenuated as well. And, puzzlingly, even the dynamics were reduced; I haven't a clue why.