I totally cop to being an old fart. I'm just three years shy of 50 (as of last month anyway). So when I started listening to music seriously, when I was around 11 or 12, there were a few formats you could get, vinyl LPs, vinyl 45s, 8-track tapes, cassette tapes, & reel-to-reel tapes. Actually, when you examine those options, there were really only two choices, vinyl & tape. I was in my early 20s when CDs were introduced. Since that time there's been a debate about which media has the better sound quality. A lot older folks, around my age, will say vinyl while others tout the clarity of CDs & mp3s. However, I'll tell you a secret; they're both wrong. Furthermore, the adage that vinyl promotes better sound quality is a total myth. Before I explain my previous statement I need to make sure everyone has the same knowledge about sound & audio technology. This will only need a pretty simple explanation, so bear with me.
First you need to know about two things analog & digital. Think of digital as a light switch in your home. You flip the switch one way & the lights are fully on; you flip the switch the other way & the lights are fully off. That's digital; a switch that's either on or off, no in-between. Digital is usually represented by either a 1&0 or by a line or square/rectangle.
Now, think of analog as replacing that light switch with a dimmer switch. This time as you turn or slide the switch the light goes from being totally off to very dim, then brighter & brighter until the light is fully on. When you move the dimmer the other way, the reverse happens until the light is fully off. That's analog; a state that's continually changing between two base values (on & off). Analog is usually represented by a curved symbol that resembles an 'S' laying on its side.
Any sound that you hear (birds, traffic, TV, etc) reaches your ears as an analog signal. Sound is analog. CDs, MP3s, & DVDs are all recorded in a digital format. Digital is great for these because it takes up much less space. The problem comes (in my opinion) when you want to make sound (analog) a digital signal. In that conversion from analog to digital & then back to analog (so you can hear it) parts of the original sound are lost forever. I'll show you what I mean.
In the picture I've provided, the green line is a sound you can hear as an analog signal. The sound is changed to an MP3 by digitally sampling the analog signal at various points. This is represented by the green & blue rectangles. Note the bits of pale yellow showing between the green wave & the green/blue samples; those are bits of the wave that are not picked up by the conversion to digital. Now granted the signal is actually sampled at a very high rate, so the missing bits are very, very small, but there are still bits missing. Part of the original sound was never picked up. Some will say that the signal has been cleaned up; I don't agree.
There is still more to be done. You want to play the sound back later. Your ears only hear in analog, so the digital signal has to be converted back to analog. This conversion back to analog is represented by the red line in the drawing. So now the signal has been stripped once in a conversion, and even more has been lost in the conversion back to analog.
Back to the myth of vinyl. When people say vinyl LPs have better sound quality, it's true... but only for LPs that were recorded in an analog format. That hasn't happened since around 1990. Therefore, if you have a vinyl LP by, say, Coldplay, it has the same quality as a CD or MP3 of the same album. So it's not the vinyl that has the better sound quality, it's the analog recording itself. Of all the formats I mentioned before (LP, 45, 8-track, reel-to-reel, cassette) vinyl is the best because tape tends to have a hiss that can never be taken out.
To sum-up, vinyl LPs are not better than CDs or MP3s, etc. It's the analog signal that's better than the digital signal. This is not only my belief. I was saying this as far back as 1986, but no one would listen to me. Then around '89 I read an interview with Neil Young in "Spin" magazine. He said that he started recording all of his stuff in digital instead of analog. He said that he did this because he couldn't stand to hear the difference in the recording anymore, so he just went to digital right off. That way he always heard it in digital, and thus, didn't hear any differences. I was vindicated then.
Oh, there is one great thing about vinyl LPs that CDs & MP3s will never have; liner notes. I know that there are liner notes on CDs. However, you have to have a magnifying glass just to read them. On the LP you can just read them. This is more of a factor for me as my eyes get older.
In the spirit of full disclosure, I must say that I love my CDs & MP3s. It's very hard to carry a vinyl LP or 45 in your jacket pocket. :) By the same token, I still have a working turntable & about 200 vinyl LPs. I'm currently working on putting all my vinyl onto my computers hard-drive.