First off, are no "Type S" Corollas, this is only a moniker that only Acura uses for it's lineup of cars. You are probably referring to the Corolla S.
AFAIK, there are no differences in the suspension setups of the CE, LE and S models, assuming that they are the same year.
In your post, you refer to two different generations of Corollas, the 1998-2002's are 8th gens and the 2003+ are 9th gens. The 8th gen models has 4-wheel independent macpherson strut setups while the 9th gen only had macpherson struts up front and a torsion beam axle in the rear.
The Corolla XRS however, does have a stiffer and better suspension than all the other models.
In your case, all that I can think of is the struts may be worn out due to the mileage differences on each car.