I've heard S2000 owners talk about how hard it is to drift the car. The suspension was setup for grip, and the car has wide rear tires. There's a video on YouTube of some Japanese guys (I think it might have been Tsuchiya even) trying to drift one, and the only way he could get it sideways was to use some pretty aggressive Scandinavian flick maneuvers. In GT6 with CH tires I only need to lightly apply some throttle going into a corner and the rear starts kicking out. Real life reviews of the S2000 mention that flooring it in a corner plants the back end firmly onto the road. The AP1 was looser, but the AP2, which is what I was driving in GT6, has tighter handling.
Pretty much all of that applies to the RX-8 as well. Car is setup for grip, very hard to drift.
There's also another problem presented by using lower grade tires - excessive wheelspin. On some FWD cars you can even faintly hear the tires squealing when driving full throttle at high speeds in a straight line. At first I thought I was hearing things, but nope, it's there.
I really wanted to think that using lower grade tires would make the game more realistic and have experimented with this quite a bit but the benefit is only in more realistic lateral G numbers. There just seem to be too many other drawbacks with most cars. I'd rather have my cars "feel" close to the real thing than try to pursue realistic numbers. This game doesn't have much of a sense of speed anyway, so the cars don't usually feel like they corner too fast on the standard tires they come with.