Club shaft question
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Well, to give you any type of accurate answer we would have to know a little more about your driver's shaft.
What kind of shaft is it (brand and model are very helpful)?
What flex is it?
Also, it helps if you tell us exactly what shaft your 3-wood has in it. Usually a manufacturer will sell a club with their own branded shaft (For example, Taylormade's RBZ Stage 2 uses their "RocketFuel" shaft by default) with the option of changing to a "aftermarket" shaft option such as a Grafalloy ProLaunch Red.
Assuming that your driver is also a Taylormade RBZ Stage 2 club, and that they both have stock shaft options with the same flex, you could expect the performance to be somewhat similar. The lesser weight of the shaft in the driver is made up for with the larger clubhead, but it means that you will feel the clubhead more when you're swinging. It just means really that they moved the weight from the shaft to the clubhead when compared to their 3-wood.
As a final note, the stock shafts provided by a manufacturer are generally not of the highest quality. This means that manufacturing tolerances (the range in which a product can be "defective" and still pass quality checks. For example, a shaft being 45.2' long instead of 45' with tolerances of +/- .5" would still pass and be called a 45" shaft) are going to be looser and the end product more inconsistent than otherwise. There is also not a universal guide for shaft stiffness. Your stiff shaft from Taylormade could be a ladies flex in another brand depending on how they categorize their flexes. Remember, tolerances also are instituted for shaft flexes too. Your 3-wood could be the stiffest shaft you can have while still being considered a stiff flex instead of X-stiff. Your driver shaft could be the softest shaft you can have that's still considered a stiff. This makes it hard to compare shafts even within the same kind of shaft if they are the stock shafts of lesser quality.