I might be able to offer a small amount of insight. I've never owned a Miata (or even driven one, to be honest) but I did go to my Brembo GT from an '08 Mazdaspeed3 and the difference was incredible. I miss the turbo sometimes but overall I have absolutely no regrets. The GT is officially the best car I've ever owned, easily beating my MS3, and an '07 Civic Si.
Honestly, when I test drove a non-Brembo, it felt alright.. not quite marshmallow-y, but it wasn't entirely impressive. But when I drove the car I ultimately bought, the improvement was clear. The physical changes are subtle obviously, with the only real difference being the quality of the tires (and I think the engine cross brace?), but the suspension feels tight and responsive. Something about the additional suspension tuning, perhaps, makes it feel that much better.
That being said, the test drives were fairly useless in terms of really getting a feel for the car. It probably took me 1000mi to feel really comfortable with it, and another 1500 to get that "oneness" that allows me to push it to the edges of its capabilities.
And even if you still don't quite feel it, aftermarket parts are plentiful and fairly inexpensive. You could probably piece together exactly the feel you're seeking for around $1500. (springs, shocks, struts, lower control arms, panhard bar).
Black 2011 Mustang GT
: MT82 - 3.73 Gears - Brembo Pkg - Boss 302 Manifold - Steeda CAI - Lethal Performance OR X-pipe - Borla S-Type axleback - MGW Short Shifter - Motiva Tuned