Sure thing. The main difference is in power outage, how much light energy the flash will produce. The normal flashgun (ie hot-shoe flash) produces between 30-100 Ws worth of output, compared to 100-4800 Ws for studio flashes.
The strobist way to "fix" this is to put in more flashguns, for example 4 in a softbox (which would then roughly be equivalent to say 200 Ws in that softbox). This works ok for smaller softboxes, and situations where you just need the flash to provide some extra punch to the existing light (either to lighten it up or to shape the reflections/specularity), but if you are going to do larger scenes, full body shots or overpower a very bright daylight scene, you may need flashes with outputs of 600 Ws or more.
Another thing that all flashes may have in common (when it comes to cheap flashes), is that the cheaper brands may differ in colourtemperature, flash duration and flash power, from the first shot to the last in a sequence. This means you will have one colourtemperature on your light on the first shot, and another on the last, which may need correcting. Can be a hassle
It all depends on what your style is (or what you want it to become) and if the strobist way (with 1-2 small flashguns) works for you, then go for it. It's relatively cheap as long as you don't have to get too many of them, and it's extreeemly mobile. Can fit the entire "studio" into one camera bag =)
And since it's batteryoperated it's very agile to work with and as the strobist movement has shown, can be used very creatively.
Going to the larger studio flashes may not be so much more expensive, but it is definately not as agile even on the best of days as flashguns. And batterypowered studio-flash solutions are generally a lot more expensive than the "normal" ones. There are also cheaper variants with battery & generator powered monoblocks but they are all heavy to carry around