I am a serious listener but don't consider myself an audiophile.  Audiophiles to me seem to be more interested in picking apart minute details in the music rather than taking it in as a whole.  Details are important for what they add to the overall performance.  High frequencies, mid range and low frequencies must also be in balance.

Vinyl and reel 2 reel are the two formats I use for serious listening.  A common mistake with vinyl is that two of the same albums will sound the same.  This is not often the case.  Different pressings, quality of vinyl used, worn metal masters, etc. all make a difference.  Two records that look the same with the same dead wax inscriptions can sound very different.  Side A of an album can have different characteristics in sound to side B.  I often purchase multiple copies of the same album trying to find the best sounding copy.  There is a company in California called Better Records that does the listening tests on multiple copies and charges accordingly.  I have purchased a number of albums from them and have found once sceptics have heard the pressings I obtained they often admit it was worth the investment.  As Hepcat mentioned, many first pressings have great sound but at times 70's repressings from labels like Decca (London) or Bluenote can actually sound better at a much lower cost.  I have very few modern reissues remaining in my collection as they can often be bettered by 60's and 70's vinyl.

I think one of the most important aspects for good sound is the original master.  This is the main reason I got into R2R.  I have obtained original master tapes, safety masters, record cutting masters, duped masters, etc. and if the original recording is not great or missing things as stated earlier they can't be replaced.  A pet peeve I have is new remastered releases where the engineer tries to "fix" a problem while often losing something else in the process.  My opinion is the closer you can get to the original master the better, flaws and all. A well recorded album with a tape as close to the original master as possible can sound truly incredible. 

I don't pretend to know as much about digital music as most but I do have my own litmus test which is simple, "How long can I sit down and listen to music?"  I don't know the reason but I have noticed as I listen to cd's or even digitally recording vinyl I get fatigued and anxious.  I begin looking for something else to do and have a hard time staying in my seat.  While I may like the material, it doesn't captivate me.  I have had many instances of listening to analog recordings on analog front ends that have lasted 8+ hours.  Time seems to stand still as each album ends too quickly.  I have never experienced this with digital.

Good listening.

ha - you funny old bugger - I've just tossed out a box full of cassettes

I do have 3 players still though - not even sure if they work.

I have to do some work connecting cassette players up to the PC with some software to convert stuff over to digital and burn on CDs. Some of it is radio programmes I did years ago. One lot with a bloke who is now dead and his mate would like some copied but no one has cassette players any more.

How do you deal with tape hiss?
Still have some old cassettes hanging around, and a player...

This is an important marker in your decline.