It must be the walking and the makeup and the hips, because you look great both ways. Such nice cheekbones! You can buy clothes and wigs and pads, and practice the other stuff, but Nature gave you a big leg up.
I do agree with the consensus here that the black one suits your coloration a bit better. It's hard to tell from just the head shots what else in your total look might be giving you away, such as whether the hairstyle suits your stature and shape as well as others might.
I've been through about 20 different wigs over the years, many just for fun but some to enhance passability (the former are the flossy ones; the latter, the more plain ones). It's hard to tell from the small photos, but it looks like you darkened your eyebrows for the black wig (or lightened them for the strawberry blonde). Good; an important detail that is often overlooked. I've used a concealer stick as a base to hold eyeshadow on the brows when I need to lighten the color. Get 'em sticky, put on the color, and brush it in gently.
With regard to hips, I, like many of us here, suffer from an anatomical condition called gluteus minimus...can you say "Veronica 2"?
You nailed that, Barbra. Loosening up, especially when we feel ourselves to be under scrutiny, is one of the last frontiers of passing reasonably well, and don't we all loathe that we were conditioned to be "stiffer [and] guarded" about letting emotions flow? Women also tend much more to have a little smile that suggests serenity and keeping a little secret.