I've come from 9 years of an F20C S2000 and to be honest the GT86 always feels a little faster. I know it isn't really, but it's a perception thing of having a little more torque lower down.
Gt86 obviously wins on comfort, practicality, fuel consumption (and oil consumption) and road noise. S2000 obviously wins on its sunroof. IMO the GT86 wins on looks too; I never really thought the S2000 was a good looking car, though that's totally subjective.
Handling is a bit more difficult as I'd upgraded my S2000 suspension somewhat and so far all I've done to the GT86 is KW coilovers but haven't had the alignment done, so can't comment too much. The 86 has a much stiffer chassis; the S2000 would flex when pushed hard even with bracing, and there's also the CoG. But the S2000 wins on weight distribution, and because there's no rear seats you're sitting close to the rear wheels and that's just more fun. Double wishbones at the front and full adjustability as stock is another big win for the S2000.
But Honda spoiled it with the designed in RWS effect; I'd replaced the rear toe arms to mostly get rid of it.
The things that disappoint me the most with this car are the gear change, which is nowhere near as good, and the throttle response. My early S2000 had a cable to control the throttle, yes that's right a cable, and that's so much better than waiting for the ECU to have a good think before it gives you any power.
I do miss mine. It had got pretty old and knackered and I decided it was time to get something newer. The GT86 isn't far off, perhaps the only thing that is, but I always tell people that the S2000 is/was the better car.