I do enjoy both, but the build is the ultimate challenge, driving is the reward. If I just bring a car back (like my profile 49) it will usually stay somewhat stock. If it's a body off, it gets modified and the sky's the limit (or wallet).
I drive my 49 a lot, 5-10k per year but when I was driving in SF Bay Area traffic, it had to be modified a little. Those that live in the Bay Area understand the types of cars/drivers we are up against, so disc brakes and radial tires might give you just enough edge to keep out of trouble.
Driving these old cars has become exponentially more fun since I escaped the Bay Area for the sticks but I do drive them back to visit parents/friends. A lot of the time driving the mostly stock 49 is the most fulfilling, there is a certain charm that gets partially lost with hotrodding.