The accuracy potential is the same. But even cheap synthetics are more consistent, stronger and more stable. Wood will always expand and contract as environmental conditions and altitude change. There is simply no way to stop this, you can somewhat limit the effects, but not prevent it. The wood stock may well be just as accurate, but as the wood expands and contracts the POI will vary. Sometimes not enough to matter, other times by several inches.
Even the cheap factory stocks are far more functional than wood. If you move up to the higher end aftermarket synthetics the difference is huge. So is the price. Prices for anything decent is going to start at around $500 and $600-$700 is where you really see some advantages over factory.
One misconception is that all synthetics are lighter. Walnut stocks, cheap factory synthetics, and even high end fiberglass stocks are all about the same weight with walnut actually being slightly lighter most of the time. The budget aftermarket stocks selling for under $400 are the heaviest of all stocks, usually heavier than laminated wood. You don't get a lighter stock until you get into the $600 stocks made of Kevlar. Here you'll often see the stiffest materials and a stock that is often 12-16 oz lighter than other typical stocks.