Which is more accurate: digital or vinyl?

"what do you feel is the more significant limiting factor for redbook, sample rate or bits per sample?"

I'm clearly not answering for Ralph, but for me I think it is the sample size that is the performance bottleneck for me, if there is one. I say if there is one becaue I still am not 100% convinced that the CD redbook format itself is deficient in any practical sense.

I say the sample size in that one of the things that I am not totally convinced CD redbook can match relative to vinyl is the ability to sustain a truly consistent level with the higher frequencies due to random variations associated with the sample magnitude value. The audible effect can often (but not always?) be subtle variations in pitch and/or high frequency transients such as those produced by massed strings, where extremely subtle transients are in play. Relatively few digital rigs do this well enough to challenge vinyl from what I have heard, but I have heard it done well so I believe it to be possible, which would mean that the implementation in play with most systems and not the format itself is the culprit.

I have heard a/b comparisons between CD and vinyl and even R2R where the analog formats clearly beat the digital, but again, I cannot say for certain that the CD format was the culprit as opposed to aspects of comparing different actual recordings in each format.

One of the most thoughtful, and poetic attempts at answering this
question appears in Peter Ledermann's answer to Neil Gader's question in
a recent interview:

"Aside from it's ease, warmth, and feel-good sound, it (analog) is
approachable, do-able, difficult, and satisfying to master and accomplish.
It is a hoop shot from across the court. Impossible to sink, but, when it
works, makes you stand up and dance. It is visceral as opposed to virtual,
marvelously and delicately ephemeral in contrast with the concrete yes
and no of digital."

I love that. I would like to offer a different perspective from what has been  
discussed mostly so far, and which points to what I think Ledermann is
saying. I won't get into the technical issues as my understanding of them
is limited, and some can do a much better job than I (thank you Ralph).
But, I know what my ears tell me, and I trust them. I believe that both
technologies are capable of excellent sound (obviously), and there are
obvious tradeoffs involved with each. I have made a living trusting my ears
for thirty five years, and their message is pretty clear.

More times than not, when this discussion comes up, the opinions as to 
one technology's superiority or inferiority revolve around tonal issues. One 
is considered brighter or warmer than the other, high frequency cut-off
points, etc. But to me, the main issue with digital vs. analog is not tonal or
timbral. It has to do with what I think Ledermann is alluding to: the feel-
good quality of analog. Whatever the issues may be with sampling rates
that many feel are responsible for tonal resolution deficiencies or
limitations with digital are, to me, even more important as concerns their 
effect on time and dynamics. Time is where the soul of music lies. The
ability to capture the extremely subtle gradations in dynamics and rhythm
that musicians use to convey a message is where the difference between 
the two technologies is most obvious to me. The grooves set up by James 
Brown's rhythm section are always a little deeper with good analog. The
difference between the softest and loudest moments in a crescendo by a
great string section in an orchestra is always more exciting with analog.
Even when digital offers a louder ultimate volume, what happens between
the softest and loudest points is more coherent, more vibrant, with good
analog. The difference may be subtle, but it is real to my ears. Those are
the subtle details that give music meaning and excitement. It is ironic,
since digital has the theoretical advantage when it comes to speed
stability. But time accuracy between point A and point B does not a groove 
guarantee. What happens between those two points seems to matter a
great deal.

There is a saying among musicians: "No-one ever got fired for
having a bad sound". What is meant by that is that what matters
most is not the most beautiful sound, but the ability to play with good time
(rhythm).

In the fields of science, engineering, industry and statistics, the accuracy[1] of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual (true) value. The precision[1] of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.[2] Although the two words reproducibility and repeatability can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.
Accuracy indicates proximity of measurement results to the true value, precision to the repeatability or reproducibility of the measurement

A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The end result would be a consistent yet inaccurate string of results from the flawed experiment. Eliminating the systematic error improves accuracy but does not change precision.

A measurement system is designated valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).

The terminology is also applied to indirect measurements—that is, values obtained by a computational procedure from observed data.

In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement.

In the case of full reproducibility, such as when rounding a number to a representable floating point number, the word precision has a meaning not related to reproducibility. For example, in the IEEE 754-2008 standard it means the number of bits in the significand, so it is used as a measure for the relative accuracy with which an arbitrary number can be represented.

RE***Which is more accurate: digital or vinyl?****

How many roads must a man walk down before you call him a man?

How many chucks must a woodchuck chuck if a woodchuck could chuck wood?

Ralph, what do you feel is the more significant limiting factor for redbook, sample rate or bits per sample? Just curious.

Well, the Nyquist theorem is looking for an exact sample (IOW with no limitation of resolution) in order to work, by definition it is the number of bits that is the real problem. When you think about it, this can only really be done in the analog domain...

My guess though is that when we can do 64-bit DACs on a regular basis that digital will start demonstrating the promise that its been showing.

I was wrong about the IBM PC being king when Redbook was devised. It was more like the Commodore 64 :)

Hifihvn, no, not unless the analog tape's sampling is very much larger than microscopic.