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Nowadays there's not much difference logistically or cost-wise between location shooting with studio monolights and battery/inverters vs. speedlight for a static two-stand key/fill lighting scenario. By that I mean you will be hauling and setting up the same stands, modifiers, sandbags to hold the stands, etc. The only real difference in logistics is the monolight and battery/inverter will weigh a bit more. But if hauling 40 pounds of sand, what's a few extra points of lighiting gear?
In terms of capability the mono-lights trump speedlights in power, recycle times, modeling light, and a wider selection of modifiers.
The only advantage of the speedlights is they are lighter which makes it practical to keep one on the camera using a bracket like this:
Raising the flash on a bracket about 16" above the lens is technique wedding shooters started using in the 60s and 70s with single flash because it hides most of the shadows and creates a very natural looking downward "butterfly" modeling without any harsh shadows. The shadows fall down below the shoulders out if sight.
In a two flash scenario that gives you good lighting in the front when you move your slave around back for rim lighting as seen here...
and when your slave is placed in front 45° from the nose the flash on bracket works as "neutral" fill that falls off front>back producing a light non-distracting nose shadow and smooth shadow-side gradient...
In terms of logistics shooting with bracketed fill and one stand is much simpler and it makes it possible to move the lighting with you vs. shooting in one spot with two fixed stands. You'll notice in the wide shots the off camera stand I use has five legs with casters. It's actually a medical IV stand not a lighting stand. Using a rolling stand light that is a trick I learned shooting weddings with two flashes. More than anything it's the rolling stand that makes shooting candids like that single-handed with two flashes possible logistically.
But in terms of capability that speedlight approach vs. the two stand/monolight approach is limited by power and modification options.
Modification of speedlights has been a bit of a dilemma. The optical sensor is on the base of the slave flash and it can't be covered up or the default signaling will not work requiring third-party radio triggers. The new 600EX-R speedlights finally solve that problem but they cost $630 each. If you went with two 600EX-Rs and wanted to use both on stands you'd need the ST-E3R controller in the hot shoe, another $420. So you'd spend $1,260 to $1,680 for a two flash solution. Then there's the problem of mounting the modifiers and the fact by making the footprint larger they cut the intensity at the subject's face by more than half. The bigger the modifier the bigger the loss.
Modifiers do do things. Directly then make the reflection of the source in the highlights larger. You get larger catchlights in the eyes which are more appealing than the pinhole reflections of a speed light, and there will be fewer specular "hot spots" in skin highlights to make the light look "hard". The other thing that makes light seem "hard" or "soft" is the gradient of highlight / shadow. The lighter you make the shadows with the fill and the more even you make the highlights with the large modifier the smoother the transitions over the cheekbones toward the ear in an oblique view will look.
Very large modifiers used close to the face and larger than the head will "wrap" the light around a face better than a small one because it comes from more vectors relative to the face. But if you objectively compare a modifier used indoors with the same set-up at night out in your driveway where there is no bounced spill you'll will see how significantly that affects the tone of the shadows, the apparent "wrap" effect of the source size and the overall look of the lighting. Big modifiers produce softer light indoors in part because they have a large footprint that bounces a lot of light around the room creating an overcast day fill effect. I call that "spill fill".
The reason I mention all this is because it explains why smaller modifers with speedlights can produce surprisingly soft looking lighting...
The dilemma I faced in the shot above was the potentially distracting white shirt. To eliminate that distraction I needed a white background. But I was at work with only one flash, diffuser and bracket as shown above. My solution? Put him less than a foot from the office wall, then stand on a chair with the top of my diffuser pressed to the ceiling. The direct flash bounced forward from the diffuser created the "mask" pattern of highlights, while the huge amount of "spill fill" bouncing around my 9' x 12' office created an "overcast day" effect which lowered the overall contrast allowing the camera to record detail in the dark hair and shadows on the face.
Most speedlight modifiers work on the same principle of splitting the light of a single flash in a direct vector and one bounced off the ceiling...
In a room with an 8-9' ceiling about equal light from both directions hit the face creating and overlapping 1+1:1 or 2:1 lighting ratio with light, flattering shadows on the faces. But that only works when there is a ceiling. When there isn't a ceiling you'd want two flashes both aiming the light directly at the subject with just the flash or forward directed modifier like a SB or my diffusers with the top flap closed as in this spur-of-moment candid "snap shot" with dual flash...
As the wide shot above of my wife on the couch demonstrates that even when the lights are aimed directly in a small room there will be a large enough footprint on the lights to create considerable "spill fill" to help lighten the shadows.
What I'm getting at here is that creating various lighting effects with flash is more about knowing how to use the tools that modify the light rather than the source driving the modifier. The power of the source equates to how far away you can shoot. That's more a factor outdoors when battling the sun than indoors.
The same is true of modification. Indoors in most cases there's a ceiling overhead to bounce the light intentionally, or unintentionally as "spill fill". The choice of a softbox vs. umbrella is predicated in part on the fact that a SB will spill less light, eliminating the spill fill variable and offering more precise control over shadow tone with the separate fill light. Outdoors or indoors in a very large or dark colored space where there is no spill fill you need to take than into consideration when selecting your key light modifier size and fill size and placement. Generally speaking the less assist you get from the "spill fill" the more you need to rely on large key light modifiers and even fill to make the lighting look softer via diffused highlights (i.e. no hot spots on skin) and light even shadows with smooth front> back fall off transitions.
In the final analysis lighting choices come back to logistics: how much gear are you willing to haul around and set up in the quest for optimal quality of light?
The solution I opted for was to have two different sets of tools: a set of four AB800 studio lights with larger modifiers I keep in my home studio and bring my subjects to when I want to optimize the light quality, and my pair of speedlights I use when shooting on location.
Why don't I take my ABs on location? Because I'm not shooting for hire and only need to please myself, not a client. But if I were shooting for hire I would use monolights and inverter, and charge enough for my services to be able to afford an assistant to haul and set-up the gear.
Look at your budget and all the equipment options that will fit it to give you a two light solution (to start). Then look at the way you want to shoot and decide if you want to be planted in one spot between two light stands, or wander around with fill over camera pulling your key light along with your free hand. If the former then monolights/inverters are a good choice. If the latter then a pair of speedlights would be better once you learn the modification tricks shown above.