Personally, I fall on the side of the "off-camera flash" category for a handful of reasons:
1. The cost - lighting can be an expensive proposition and purchasing both studio strobes and off camera flashes (for location shoots) simply doubles that cost.
2. Laziness - I did not want to take the time to master two distinctly different lighting systems and then have to take the time to "think" about which lighting system I was using at the moment and how I needed to set it up. By using one lighting system in all situations it became second nature more quickly, I am thinking about the shot, not the equipment.
3. Power - I don't have to worry about where I am going to get power when I go on location. Often people will say "but you must go through batteries so quickly", not true, rarely do my flashes fire at full power, usually they are at 1/64 or 1/128 power which means they cycle quick and shoot forever.
4. Flexibility - with a single clamp I can put a flash in places you could never get a studio strobe.
5. Safety - Everything is wireless so I have no cables to deal with, and often no light stands either. My flashes are clamped onto doors, bookcases, sitting on table tops, etc.
6. Space - There are shooting scenarios that simply don't have the room to use studio strobes.
7. Portability (this is a big one for me) - my "bag of light" is a Tamrac 614 and is stuffed with everything I need: 2 SB-800's, 3 SB-24's, 5 pocket wizards, diffusers, gels, rechargeable batteries, 1 Quatum Turbo, 1 light meter, 1 rocket air blaster, lens pens, several Lumiquest light modifiers, different size reflectors and diffusers, 3 table top light stands, 2 mini stands, 2 shoot through umbrellas, and a partridge in a pear tree. Try getting that much studio lighting power in such a small space.
Alright move away, I am now stepping off my soap box.
;)
I know that there are many good things about studio strobes (like the amount of light they can throw) and reasons to have them, I'm not saying that off camera flashes is the only way to go, it's just the only way to go for me.