Software could never get rid of all the effects of distortion. The reason is that, if you do not operate in the hardware level, you could only make approximations about the real effects. Distortion models such as pin-cushion, barrel and etc are only the effects which we could model.
The distortion removal techniques, which are based on some kind of supervised learning might do a better job, but even what they learn is an approximating function and not the actual physical model.
Having said those, software could do a pretty descent job of handling distortion. Yet, I'm afraid that 180 is significant. Of course, on the other side, you would have the stereo stitching artifacts. The choice is dependent on which one you care about more. Stereo would probably have less distortion related issues, but the calibration errors and seams will degrade the image quality. It is best to try out for the particular choice of a wide angle and stereo cameras.