i'm one of these people which uses (or should that be... used to use) a stofen outside.
i found that using it at the shorter focal lengths softened the shadows a bit.
anyway, i did some experiments over the weekend after seeing this thread on my phone and i have to say.... i didn't notice any difference between an exposure with it on and an exposure with it off.
i'll try to post some pictures later.
I've done that too, but I've not posted any pictures because there's nothing to show. Zip.
An A-B direct comparison is the only way. People sometimes say they notice a difference with a Stofen, but there's never any comparative evidence, with and without, to go with it.
Flash is very dependent on the environment, even naked direct flash. For example, if you shoot an identical subject in a small, light toned room, and then outside, the light on them will look quite different, and also the flash exposure level will drop by up to a stop outside. The flash looks much harsher outside, and there is zero fill-in coming from surroundings.
I have also noticed different effects depending on what I'm wearing! Shoot a subject in a white top when you're also wearing a white T-shirt and the flash bounces off them, back to you, and back to them as nice soft fill-in! That can make a big difference, your own built-in mobile reflector
With a Stofen outside, I also shot the same subject standing on a light grey patio to see if anything came up from that. It didn't. I even put a big white towel down to try and force some kind of reflection, but even that did nothing unless both the subject and I got down on one knee, a couple of feet from the ground.
Outside with a Stofen the only differences between that and direct flash were, a) the shadows move slightly because the flash head is angled up a bit higher, b) you instantly lose at least three stops of flash power. Gone into nowhere. Otherwise the images are identical.