The S2000 and Miata have completely different characters. And therefore, in my mind are two entirely different ownership propositions.
The NA/NB Miata is more playful at lower speeds. You can have fun in a Miata at 6/10ths, which means you'll be able to enjoy it more often, with less serious consequences. That is the magic of the car's formula: you don't have to break the law or kill yourself to have fun. The downside of that is that I've never felt the car keeps up with your commitment level. It is predictable and (famously) easy to toss around, but lacks the ultimate edge at 10/10ths and beyond.
The S2000 is a much more 'serious' car and requires --no, demands a higher degree of commitment before its considerable talents shine through. As other have already pointed out, at 6/10ths the car is simply not very interesting. One thing I've always disliked about the Stook is the steering (which is electric); it is precise to a few hundred decimal places, but offers almost no feedback. You do, however get lots of feedback through the chassis, which is ultimately better than the Miata's, IMHO. There is less slack and more body control in the Honda. And once you have the motor on boil, there is simply no comparison. The S2000 will take you places the Miata simply can't.
Drive like you are qualifying and the S is the better car. The question is how often you can and are willing to do so.
And it is well known the AP1s have a strong tendency for lift-throttle oversteer. This is either a blessing or a curse, depending on the disposition (and skill level) of the person driving it.
I think anyone considering the Miata should just get a Miata. There really isn't another roadster that does what it does, as well as it does. However, anyone strongly considering an S2000 should also take a close look at the 986 Boxster and Z4 --both these cars have abilities that overlap the Stook and ostensibly have the same mission. But the performance is more accessible and less 'peaky' in the Porsche, IMO.
And I think someone wondered if early Boxsters break all the time: yes and no. The tops break all the time. And because its German, some electrical stuff breaks. But not counting RMS issues, the basic cars are fairly solid. The RMS is a whole 'nuther issue I won't get into; but I think it happens about as often as Stooks grenade their differentials.
M