The new casks that are used for bourbon tend to translate into a spiciness that I don't often find in Scotches. Even then, sometimes that spiciness comes from rye in the mash; the high-rye-content Old Grand-Dad 114, for instance, has an intensely hot cinnamon note to it. Yet Old Rip Van Winkle 15/107, a wheated bourbon, was also quite spicy to me.
Even so, wood can crop up in Scotch as well, in a different way. Ardbeg 1977, for instance, combines its peat with an oak forest.
It isn't spicy the way that bourbons can be, but IMO, the result is magnificent.
Most of the spice/vanilla notes from bourbons come from the "red layer" where the charcoal and unburnt wood meet. The woodiness that I find in, for instance, the A'77, most likely comes from tannins.