That's actually a more complicated question than you might think.......
The answer really depends on several things:
1) What the original quality really was
2) Where along the process your "master" really comes from
3) How much work you're willing to put into it
For example, if you have an original multi-track master tape, then you have the opportunity to completely re-mix it. When a multi-track recording is mixed, each track may be processed separately, then they are mixed together, then the overall mix is again processed. And, it is quite possible that modern technology may in fact allow a new re-master to sound better than the original tracks, or simply better than a previous mastering. Along the way in the complex process, there are lots of places for things to go wrong, or right, and lots of things that could be re-done differently. Check out the description of what was done to remaster the Grateful Dead Studio Albums (n the version they sell on HDTracks) for an example of this. On certain albums, special processing was even performed to "repair" timing variations on the original master tapes. The result was that the new versions of some of them sound very different, and much better, than the "originals". So, yes, it's entirely possible for a "re-master" to end up sounding significantly improved even over the "original master". (And, if you've bought "re-masters" before, you realize it's also possible for the new version to sound significantly worse as well.)
Even if the starting point is an already-mixed stereo master (or a recording that was only ever done in two channels), there's still the possibility that a modern engineer, using modern equipment, may be able to improve on the original by doing a better job with the EQ, or possibly by applying good quality noise reduction (but, of course, no guarantee that the difference will be an improvement).
And, yes, some of the early D/A converters used to master some of the early CDs simply weren't very good - in which case simply re-doing the conversion process with a modern converter, even at the same sample rate, may in fact make a huge difference in sound quality.
And, finally, one thing that many people don't realize is that there sometimes
are benefits to be had by improving the quality of a copy even beyond the quality of the original - and even if the quality of the program content itself isn't improved. For example, if you have an original that has a lot of hiss, and you've decided that it isn't practical to try and filter out that hiss (because any filter able to do so would also damage the content itself), you may still find that the background hiss itself - annoying though it is - sounds less annoying when reproduced more accurately. (As weird as it may sound to someone who hasn't tried it, if you start out with an original with very little high frequency content, and lots of hiss, the best sounding option may be to filter out the hiss; however, if your original has lots of hiss, with some legitimate high frequency content mixed in with it, it often sounds better to leave the hiss; and, if you choose to go that way, then reproducing the hiss more accurately can actually result in it's being less annoying and distracting than reproducing it poorly, and in your being more able to "hear the content buried in the noise" and having it sound more or less natural.)
So, to take a not-uncommon situation, let's assume we are starting with a master tape that has quite a lot of hiss. When someone cut that master tape onto vinyl in 1960, the hiss from the tape was simply added to the surface hiss from the vinyl, and the result was an album that was a little noisier than usual - but, other than that, it sounded "pretty normal". Then, when someone re-mastered that tape to CD in 1980, it was probably with the expectation that "customers expect the digital version to be quiet and have lots of high end". As a result of that, it's quite possible that they applied some pretty aggressive filtering to remove the hiss, and then some boost to what remained of the high end, in an attempt to make it sound "clean and quiet". (And the result of all that may have been a CD that sounded "clean and quiet" but also "a little bit odd".) In that situation, it's quite possible that a modern remaster may sound significantly better - either because they decided to leave more of the hiss in (so you've got a more accurate rendition of the original master tape), or because, while they applied even more aggressive noise reduction, modern software does a lot better job of removing hiss without damaging the music. (And, even if there isn't much high frequency content in the music, accurately reproduced hiss may actually sound much more "benign", and be less annoying, than inaccurately reproduced hiss.)
You visually see this situation quite often with re-mastered videos.... where, even though DVDs are far less noisy than VHS tape, a VHS tape that is
badly remastered onto DVD actually ends up looking worse than the original VHS tape... and then a later, more well done, remaster looks significantly better than either.
Therefore, I would always advise people to avoid making any sort of assumption with a remaster..... read the reviews; read the descriptions about what was actually done; and decide whether it's worth buying each one on a case-by-case basis.
(And I personally recommend the Grateful dead Studio Albums...... )
Logically speaking, what benefit is there to a recording in a higher resolution that what the original was recorded at? HDTracks releases all these older recordings in hi-res but the limitation is the original recording. If there is any difference, it would be due to remastering or remixing, not from the actual resolution. My opinion, most of what is there is just to make money from the current fad of everyone going after "hi-res" and whatever that means since it has become mainly a buzz word for most people.
