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Depends how you use the natural light. With sun at the backs the sky and front of the subject is in shade the flash becomes frontal fill and flash is creating highlights over top of it. As a result the flash modifier doesn't need to be as big and wrap as much as indoors where you don't have that foundation of wrap-around soft fill.
If you add a second flash over the camera as fill to control the tone of the shadows (skylight alone renders them quite dark when sunny highlights are exposed below clipping) the off axis flash winds up overlapping sky + flash fill. The primary cause and effect resulting from a larger key light modifier will be larger catchlights and smoother less specular skin highlights. The effect of the modifier size on the shadows will be less because the sky and the fill flash will trump any wrapping effect.
You can see this for yourself with a simple comparison test outdoors. Set up a subject in white shirt in backlight (face totally in shade) in an oblique view with fill over the camera and key light 45/45 from the center line of the nose (key will wind up 90° from camera axis).
Start with a baseline ambient only shot, exposed SUNNY 16 to keep sunlit parts of shirt below clipping. First add direct flash from the key light until you get a highlight pattern on the face that looks normally exposed relative to the sunny parts. The shirt will help you visualize the balance. If its not clipping on the back in the sunny parts you see it will need to be a bit darker than you would expose it indoors with flash in the front to retain the ambience.
When you get the highlight exposure on face and shirt balanced to ambient backlight note the appearance of the highlights (specularity) and the tone of your shadows from just the sky fill.
Next add the fill flash from over the camera (flash on bracket works good for that) again with direct flash. Raise fill until you get a ratio you like by eye. You will find as you add fill you will need to reduce key flash power because they overlap.
When you get the exposure and ratio balanced to taste in front on the face and shirt again note the appearance of the highlights (specularity) and the tone of your shadows. You will find that even with direct flash the gradients of contrast on the front of the face are quite smooth. That's because God's own SB, the northern sky is providing a foundation of wrap around fill that the flashes complement and lift instead of fighting. It's a real eye opener regarding the underlying cause and effect.
Now from that direct flash baseline add modifiers to the set-up. FIrst just to the key light. Compare against the direct flash baseline. You will see more change in the character of the highlights, less in the shadows.
As you try bigger and bigger modifiers you will reach a point where the logistics of wrangling them in the wind trump the difference vs smaller ones in the character of the lighting. You may conclude that you can get by with a much smaller modifier than you assumed before the test. The test is necessary because you need side-by-side comparison of images to grasp the subtle differences.
For whatever size you find works pluses of a SB vs umbrella are shape ( you can pick a round or square SB) and reflection of the source in the catchlights (the ribs of an umbrella seen in the catchlight reflection can be distracting) and efficiency (smaller foot print, less of the power wasted lighting things not in the photo).