I think the correct answer to this is both! Refinishing can have a bad effect on the horn and it drives away the collectors. A poorly relacquered Selmer can definitely have a negative impact on the sound. Sometime it gets a bit thin sounding. Other times it will loose the center or make the tone less even up and down the instrument. However, that's not necessarily the case with a relacquer that's well done.
Any Selmer that has been relacquered has been buffed in the past. This process removes a layer of metal from the instrument. This is why the engraving is typically less pronounced on a relacuered instrument. In fact, the degree to which the engraving is buffed down is a key indicator as to how careful the person doing the buffing was. There are several other tale-tale signs of buffing as well besides just the engraving. The process for refinishing a saxophone is as follows:
1. dent work and key fitting
2. strip existing original lacquer
3. hard buff
4. color buff
5. degrease (the best is to use a vapor degreaser with trichloroethylelene)
6. apply new lacquer
Its steps 3 and 4 that really determine the quality of the relacquer job. A well done relacquer will remove very little metal and the result can be excellent. For example, saxophones that were sent back to Selmer for an overhaul (back when Selmer had a saxophone overhaul shop in the 1940's-1980's) are sometimes almost impossible to discern from an original lacquer horn. In fact, we have a 38xxx Selmer SBA tenor in the shop now that is one of the best factory relacquers I've ever seen, It actually plays better than the two original lacquer SBAs that we currently also have in inventory. Its so good that many would probably argue that its actually original lacquer.
That being said, all saxophones have been buffed as part of the manufacturing process. Check out the video on this site that shows the manufacture of a Buescher saxophone in 1924. So, there is also variation amongst original lacquer horns in terms of how hard they were buffed. Its just that there are no outward signs when the sax is in the original finish.
The bottom line is if considering a relacquered saxophone be sure to have it inspected by an reputable expert repair shop first. There are other issues that can plague relacquered instruments depending on the instrument's history. These other problem issues are often overlooked by the unsuspecting buyer by the sight of a shiny new looking horn. Things we look for on all relacquered saxophones include buffed out key work, buffed or filed tone holes, worn pearls and/or pearl holders, bent keys, patched or otherwise repaired neck, mis-aligned tenons or solder joints, presence of non-original parts, over-buffing, etc.....
Last point, is that the price difference can be much greater than $1000. Depending on the vintage and condition of the sax a relacquered Mark VI could sell for as much as $5000 less than its original lacquer counterpart. There's definitely a good spread in price range and many things to think about here. Best of Luck!!!