Vinyl noise tends to be music genre-specific and/or equipment-related.
In this regard, recordings of solo performances such as solo piano tend to be problematic, as opposed to boisterous rock / pop recordings, which almost always out-shout noise.
As for the role of equipment, some cartridges and styli emphasize surface noise. Elliptical styli, which are used on the vast majority of modern cartridges, have a small contact area and wear a trough at the contact patch in the groove, and the trough gets worse as a record is played repeatedly. High-tech line-contact styli, on the other hand, are basically shaped like the groove and touch much more of the groove, playing parts of the groove that have never been played before and that have experienced no wear - depending upon the geometry, they can ride over the trough cut in the groove by elliptical styli and make even very used records sound new. Also because of the much greater contact area, line-contacts cause much less wear (the pressure is distributed over a much larger part of the groove wall, greatly decreasing wear). The following link shows a picture of the forerunner to the line contact, a Shibata, compared to an elliptical (scroll down to the black and white photo):
http://books.google.com.au/books?id=9OEDAAAAMBAJ&lpg=PA66&dq=phono%20cartridges&pg=PA66#v=onepage&q=phono%20cartridges&f=false
Modern high-end tables tend to have very little rumble and thus minimize noise compared to modest tables or mass-market vintage tables.
Poor cartridge set-up, which is extremely common and the biggest problem with vinyl in my opinion, can greatly increase noise. In fact, it is precisely the line-contacts that are hard to set up, as they can only lay in the groove one way to fit - imagine a big "V" sitting down into a little "v" (it won't "work" unless it sits just right in the vertical and horizontal planes).
As for PCM digital, it's fine for low frequency and midrange signals, as such frequencies oscillate relatively slowly compared to PCM's 41,100 times per second sample rate - taking 41,100 "snapshots" per second of, for example, a signal that cycles up and down only 400 times per second (a 400 Hz. signal) will capture such a signal's path with great accuracy, but a 41,100 per second sample rate is inadequate for high frequency signals oscillating at close to the same speed as a the sampling rate - it fails to capture most of the arc of the signal, which is why a PCM recording of orchestral music, with all of the high frequency overtones coming off the string section, sounds unnatural and fatiguing on a high-resolution system. Imagine a camera with a slow shutter speed trying to photograph a jet aircraft or bullet in flight.
Vinyl noise tends to be separate from the music, while PCM digital's problems are woven into the fabric of the music - it's like somebody pissed in the soup and then osterized it. In any event, a reasonably clean LP of most types of music played on a good quality table and cartridge that have been properly set-up, especially where the cartridge uses a line-contact stylus, will not present noise problems (... but I'm the first to admit that all of those conditions need to be present).
