That's the same question my local camera shop asked my when I told him I was looking for a basic studio setup. In a nutshell, continuous is signicantly cheaper, but can get hot over time, like Snownow said.
For my product shots, its not a problem, but I would hate to put a person under those conditions for a long period.
I ended up with a basic Smith-Victor kit consisting of (2) 8' aluminum, (2) 500-watt bulbs, 10" reflectors, and 32" umbrellas for about $140. I was told that I could easily replace the lights with a few SB-800s (wired or wirelessly) with my D200 to get a basic strobe setup. I haven't tried that yet.
Strobes. They are cooler, more efficient, more controllable (variable output settings), and can light anything.
That being said, hot lights can work if needed. The first photo studio I worked in (Allen Snook Studio, Chicago; 1979) shot food photography, with ice cream as the specialty. We used a single 500 watt tungsten bulb (with bounce cards) on everything (and used only 8x10 film). The results were superb (about 50% of the images on ice cream packages in the frozen food isle were made by us, and I bet many of the images are still in use).
I work in TV news for a living so I know a thing or two about continuous lighting. I had a 2 camera shoot earlier this week. It was in a 16x16 room and I was dying after the 45 minute interview was over. Not to mention I burned my hand breaking down for the umpteenth time.
Call me an old fogey, but I use a set of Norman hot-lights. I often use different light sources so having continuos lighting helps me get the balances just right. I also put large polarizers over the lights. I need continous light in order to see the effect correctly (modeling lights are at a slightly different position that the lamp in strobes.)