There are two fundamentally different types of noise reduction systems that were developed for LP records. The first deals with removing the annoying ticks and pops heard when the stylus plays through a scratch or gouge in the record groove. This is an impulse type of noise. There were external analog noise reduction units sold that were wired into the stereo through the the tape monitor loop that did a pretty good job of removing these transients from the music. The problem was that even after careful adjustment of their settings, while removing the annoying audio artifacts of the scratches, these noise reduction unist also tended to audibly affect the music by removing some of the transient peaks. Still, if you had a record that was irreplaceable and also had some bad scratches on certain tracks you could play the treasured recording through the noise reduction unit while making a copy on cassette or reel to reel tape.
The other type of noise reduction, most often seen as the DBX type I and II compander (compression/expansion ) units, were used when playing special DBX encoded records and tapes. With reel to reel and cassette tapes the goal was to reduce the background tape hiss noise on home-made recordings to an inaudible level, resulting in better noise reduction than the consumer Dolby B encoding. With vinyl the goal was to reduce the background 'whoosh', the noise of the stylus running through the groove of the record to an inaudible level and to capture the wide (70-80db) dynamic range of good classical or jazz recordings. This required purchasing special DBX-encoded LP records. These LP records included a fairly small catalog of popular and special audiophile recordings. Many of the DBX units also included a feature to recover some of the dynamic range from conventional range on conventional LPs, usually in two or three separate frequency bands (to avoid obvious pumping up and down of the the audio level).
At the time most LP records had a dynamic range of perhaps 55dB, and audiophile recordings such as Telarc maybe 65db. Since most pop/rock music was/is highly compressed for dynamic range, there was no real benefit of the DBX system with these types of recordings. However, for certain classical music orchestral works, the ability to capture up to a 90db dynamic range was a big improvement not equaled until the CD format was released.
The DBX LPs did sound quieter than a standard LP, even quieter than a clean Mobile Fidelity or Telarc LP, but the selection of DBX titles was short lived and limited. Also, perhaps more of a problem on tape than on LP, the 2:1 compression and 1:2 expansion function of the DBX system on the dynamic range of the program tended to result in some audible pumping up and down of the background noise as the music level varied. To be sure this was only audible on quieter passages, but that is the only time when record and tape noise is a problem for most listeners anyway.
To me, the sound of tape hiss or LP record groove noise was never much of a problem because it is fairly constant in level and spectrum and the brain soon learns to filter this noise out of the listening experience. The ticks, pop, and scratches caused by dirt, dust, defects, and scratches in the surface of a vinyl record were always far more annoying, especially when listening with headphones. This was one of the big benefits of trading up from vinyl to CD.
Today, with good amplification and headphones, I can hear what was lost from the older analog tape and LP sources when the music industry moved to CD. Over time, CD players and CD mastering has improved, and I see much promise for future formats such as SACD (closest thing I have yet heard to good reel to reel source) and DVD-A (I've have not heard it yet). Analog playback systems have improved too, so if you are willing to put up with the rigors of vinyl (cleaning, handling, storing, and playing) records then you can still enjoy what many consider to be a superior music format.