Studio lights have faster recycle times, are more powerful, can use modifiers, have modeling lights etc which is true. But sometimes it's not particularly practical to lug a vanful of gear and generator when you've only got few minutes to get the shot done. Speedlights just go on stands and you can put them where you want, nice and easy. Theres a set of tools for every job and it seems like the Strobist style has a clear advantage in terms of ease of use and portability when working outside.
Also there is a myth that the 'strobist' approach is cheaper. Really, two AB800 with some modifiers and light stands can be purchased for less than $800. Two 580EXII's/SB900 etc with their triggers are around $899 sans stands or modifiers.
Having used all kind of gear, I have to say that both work. Knowing how to use both makes you more flexible.
So which is better?
The answer is to use the right lighting equipment for the job. It's not about getting the job done 'faster', it's about having full control over the lighting and the choices that brings to the shoot. It's also about having the amount of lighting power that you need so you can fit the proper light modifier to the job and so that you aren't limited to shooting everything at f 5.6.
ON A SIDE NOTE
For those who are pro commercial photographers and even advanced enthusiasts know that when you have all the lighting tools at your disposal, you can do any lighting effect. eg.
To create a clean light with soft shadows....a large octabox is ideal.
For a dark moody look with lots of shadows....a grid or small beauty dish with flag will give you the effect.
For a beauty shot....large beauty dish with reflector or para light will do the trick.
For overpowering the sun.....a powerful battery pack.
For the ring flash look....um...a Ring Flash.
For Jill Greenberg/Dave Hill look......lights blasted from all sides of the model etc etc
I've recently followed the Strobist philosophy of "Less Gear, More Brain, Better Light" and decided to keep it simple and go with just a single speedlight with/without umbrella for a couple of shoots. Making all the limitations into a photographic style, it has been an enlightening and a fun process. Here are some resulting images:
The thing is, when you are armed with just a single flash, you have to use your creativity and whatever ambient situations to get the best of the situation. The ability to convert these obstacles and limitations into an amazing photograph helps develop the spontaneity and skill of a photographer...... and in turn, a personal and original style.
Light is light. It doesn't matter if it comes from the sun, a street/shop light or a strobe. How you shape it and control its quality and intensity from the subject is what creates a photograph. Low-tech lighting is fine but it seems like it is ironically suited more for the developed photographer trying to make a point. Take a look at Steven Meisel shooting Bottega Veneta 09 Campaign with a speedlight ON camera and an H.M.I for the backlight in the mix.