The differences would be just noticeable in a back-to-back test on a race track. A 2007 or 2008 S2000's OEM shocks will no longer be at their original settings, bushings will have worn, etc.

Most people modify to different shocks/springs unless they are competing in a class that requires stock springs, such as B/Street. I posted a link to a presentation that discusses the difference between different shocks and their designs. Similar to virtually any professional race car, the OEM shocks and most third party (except KW and Koni) are monotube. The OEM shocks and some others determined that the short rear shocks don't have enough volume for the nitrogen, especially if lowered. The OEM shocks have a piggyback chamber in the rear, Penske recommends an 8300 with external reservoir if lowered. PSI did it for their S2000 version of the Ohlins TTX shock.

 

It's a good idea to live with the stock suspension for some time to get to know it and adjust your driving style to fully take advantage of the car's potential. That said, I think you're going to find that it's going to understeer on the autocross course. You may be able to provoke oversteer depending on tires, but these engines are not torque monsters so it's a bit of a challenge. Regardless of which car you choose, I'd recommend adding as much camber in front as the stock suspension will allow to begin with. Depending on what that gives you, you may want to add offset ball joints to get more.

I have a MY00 which everyone said would oversteer, but that wasn't what I found. The rear end did move around due to toe changes over bumps in turns, but otherwise it understeered - just like most cars with factory suspension settings. Going to 3.2 deg up front made things a lot better on the track. And that's for the MY00. I think you'll find the later years you're considering will understeer when pushed hard.

In summary, I wouldn't worry too much about the suspension differences between those two years as you're likely to make other changes to meet your goal of no understeer on the autocross course.