If you want something that's as good or better than the original then scanning is the best way forward.
??? ??? Better than the original? As good as the original?
Umm depends on how you define 'better' and 'good' I suppose .. but in technical terms every stage of the analog reproduction process introduces degradation (noise, distortion etc) thus you cannot 'improve' on the original? Removal of things you may not want/like may be seen as better but in terms of preservation better off with the original.
It's rather easy to define, and I thought I had in a previous post?
Essentially, if you look at most photo restorations, there are some good ones on this site, you will instantly see an improvement on the scan. When I mention an improvement on the original I am referring to that original scan, which in many cases will be damaged.
So obviously a scanned and repaired photo is going to be better than the old damaged photo.
Clearly it would be difficult to produce something better than the day the photo was taken but since that is a hypothetical situation that will never occur because many of these photos are decades old it's safe to say that with scanning and editing an old photo you can considerably improve on the old photo.