Thanks for adding to this discussion. And for posting the two images to consider.
I prefer #2 (Big Light).
I think it looks much better for a few reasons:
1. Not such a tight composition (the #1 image is too close)
2. More \"ambient\" light and background (even if OOF, the background gives depth)
3. Nice expression, seems friendly
4. Light on face seems softer and nicer, pleasing. Looks like reflected light from a table top outside in an open shade environment, using the sun for ambient and possibly the reflected fill. So, it looks \"natural.\"
5. The light in the eyes looks nicer, not just a spot/dot (catchlights) as shown in #1 image
Another observation about the second image: it has a hat. When people wear broad brimmed hats, the eyes and foreheads are often dark in shadows. Your second image has very nice even light under the hat brim and looks much better than most images of a man wearing a hat.
The second image looks good, regardless of light source or technique. It is a nice portrait.
That said, there are other differences too. The first image appears to have been made inside in \"close quarters.\" The second image appears to have been made outside. The technique I described earlier as \"FoolProof Flash for SelfPortraits in Close Quarters\" could certainly be applied to some outside situations (if seated next to a large wall or reflective surface for instance), but it is really \"geared\" to using small spaces as typically found in a home or apartment to \"bounce\" the light from a flash in order to give a larger light source and better light and angles on the face.
So perhaps a better comparison (of two images) would be a more \"confined\" space (like a typical bedroom) and the use of one, two , or three white walls nearby. One shot to show the flash \"direct to face\" and the other shot to show \"flash pointed at wall.\"
Finally, was the second image shot using the flash method described in my original post?
