Hi Stan, based on knowledge of the Series 1 circuit schematic, the voltage really should not change the sound. It only raises/lowers the maximum possible output level.
For reference:
- On batteries, you get a total of 18V from two 9V batteries.
- My DS-5 actually produces a total of 42.1V from my measurement, but there might be some slight differences between different units. The exact number doesn't make a huge difference though.
If you are using batteries, and you turn up the gain and/or volume to more than the 18V can handle, I think it's possible that you might get some output clipping (distortion). It's been a long time since I tried, so I can't remember if this is even possible, but I think you can get some clipping if you really max out the gain on the internal trimpots and use it with batteries only.
It should be pretty obvious that this is happening, though. If you keep the gain down to within a more "normal" range, I can't think of any reason why there would be a difference in the sound between batteries and power supply.
Mine can get plenty loud on batteries only, and the actual volume difference between an 18V supply voltage and 42.1V is less than you might think, due to many other factors. So I personally feel like batteries are fine sound-wise, it's just a pain (and not very eco-friendly

) to go through so many of them.
Good luck!