In years gone by, gunsmiths would take military rifles, usually a Mauser, and sporterize it. Some were artisans who bedded barrels full length of the stock, often using the finest woods, checkered beautifully, engraved metal, etc. They were works of art, but many didn't shoot as well as some tuned factory rifles.
One guy, a good, older and richer friend had a beautiful custom rifle and he tried to win a turkey at the local shoot. My wife and I couldn't get to the match until later in the afternoon, due to a family party. When we got there, he had come in second closest to the center of the 100 target 10 TIMES. My 7 month pregnant wife beat him by shooting a perfect pinwheel on her first shot, so he came in second again. On a bet by the other guys the previous week, I had taught her how to shoot early that morning, lying down and resting the rifle on the log.
Custom today often means the best barrels and actions, stocks, scopes, triggers, etc. Depending on how they're put together and fed, some are truly marvels. The gunsmith guild members are often still not into accuracy that much, especially when judging the several rifles that must be built for certification.
The moral of this story is: Choose your gunsmith wisely and make sure you get one that has a proven record of accuracy, if that's your goal. If time a big factor for you, you may not want to have a rifle built for you, but have a factory rifle accurized, which shouldn't take as much time.