On the face of it this topic appears to be madness, however there is definitely some science behind it.
A perfect power supply will deliver a constant voltage regardless of the current delivery. Most pedals run on 9 volts, and this delivered either by a battery, or by a mains adaptor, which is often unregulated.
A new 9 V battery will deliver around 9.5 volts when new, but will quickly drop to under 9 volts, and gradually run down over its life span. However, batteries have one major advantage; they have no AC component, and thus will not inject noise into your pedal. Batteries also have a significant impedance which will drag down the voltage at higher currents. Most pedals draw fairly low and constant currents, so power supply sag is not so much an issue here.
Many mains DC converter are unregulated and will deliver much more than 9 V when lightly loads. An unregulated 9 V supply rated at 100 mA will deliver 9 V when 100 mA is drawn, BUT will deliver much higher voltge at lower current draw, perhaps as high as 12 Vs!. Additionally, a small amount of AC ripple might be present on the supply rails.
The AC ripple is not a problem on many effects pedals eg those that use OP amps as these have an inherantly high power supply rejection ratio, so are oblivious to a small amount of ripple on the power rails. However many single ended effects, eg Fuzz faces, and many germanium treble boosters are very suceptible to power supply noise. A poorly smoothed DC supply will inject significant noise in these type of pedals (although many Fuzz Faces don't have DC adaptor sockets as they are ground +ve).
Furthermore, for many analogue pedals the supply voltage can have a significant effect on the overal sound of the pedal. Higher voltages will provide more headroom in analogue pedals, and this be particlarly noticable in distortion pedals.
There are several regulated power supplies on the market (which use 3 terminal reguators) eg the Voodoo Labs pedal power, but these are more expensive than unregulated supplies.
So what's the point of this post? Well when comparing batteries with a DC mains adaptor make sure you are comparing like with like. An old battery delivering 8 volts, will almost certainly sound different to an unregulated power supply delivering 10 V in a distortion pedal. From my experience it is the variation in voltage that makes the difference.
From my experience of adding DC adaptors to battery nonly pedals, building pedals and listening to various pices of equipement, I tend to prefer pedals run on new batteries oir from a DC adapotor, although I can see why some people prefer to run their pedals of older batteries.
Also bear in mind that pedals that are buffered and not hard bypass, such as BOSS and Ibanez pedals, can sound bad when OFF with a low battery. Not good.
The other day my band members and I were listening to a two TS-9s that we had converted to TS-808 spec using either an NOS JRC4558D or a reissue JRC4558. All three of us were convinced that the NOS JRC4558D sounded better. However, just to be 100% sure we swapped the batteries over and low and behold the reissue JRC4558 now sounded better. Thus we concluded we should get out more!
Hope this is helpful.
