I've had three AE86s total and had at least one since the mid-90's. I've driven friends JDM cars and the only thing you'd notice in terms of different driving experience is which side the steering wheel is on.
The North American cars are "real" AE86s, just like the Japanese models. The mechanicals are generally 98% the same. In Japan they got the choice of pop-up lights on the Trueno, or fixed lights on the Levin, and all of North American cars came with pop-ups. All of European cars were fixed. Japan and America got a choice of hatchback or coupe, and Europe got all coupes. These differences are almost purely cosmetic. The hatch has easier loading for cargo, and the coupe is a tiny but quieter on the highway, but the difference in feel behind the wheel is minuscule.
Here's the little detail stuff that won't really change the driving experience much, but you might notice if you start crawling all over both Japanese and American versions side-by-side:
Less crash-protection and less safety for the passengers on the JDM cars. The bumpers and door beams are essentially non-existent. They are a touch lighter, but not worth obsessing over.
More trim levels available on the Japanese cars. We got the base singlecam DX, singlecam SR5, and performance GT-S with more options. In Japan they got some total stripper cheap singlecam models below our base spec, some versions aimed at the young women, twincam GT and GT-V performance models that are fairly similar to our GT-S in terms of performance/driving experience (4AGE engine, stiffer suspension, swaybars, disc brakes, optional limited slip, etc) but often have less of the comfort/convenience features that many (but not all) of the U.S. market GT-Ss came with, like power steering, electric mirrors, sunroof, A/C, rear wiper, cruise etc. Japan also got a range topping Limited model with special trim, power folding mirrors, digital dash, and a few gimmicks we never got.
JDM ECUs measure incoming air with a MAP sensor. American cars measure incoming air with an AFM. The condition of the 30+ year old engine will have a bigger impact on what the car is like than the tiny difference in how the ECU measures air....if the car in question still even has the original parts. The other differences mostly have to do with different legal requirements in diffferent countries, like different side marker lights, different emissions equipment, etc. Once again, an aesthetic difference, and your preferences and condition of the car will be the biggest factors here, rather than the theoretical superiority of one over the other.
So many of these cars have been modified and had parts swapped around that discussing trim levels and factory options on American cars is a purely academic exercise at this point. JDM cars might be found closer to stock, but not always.
I can go into more detail if you want. Hope this helps! :D