They are not "E-Class" since the "E" in the 190E, 300E, 400E and 500E is the German word for fuel injection, eizenspritzer. Hence the reason why there are D versions for diesels and no designations for the carburator version.
The are different sizes of basically the same platform. The W201 is considerably shorter in wheelbase and overall length than the W124. They share many common design elements, most of which were derived for the W201. During the design phase of the W201 it was decided to keep it RWD and to take advantage of some suspension part sharing between the two chassis.
As far as performance and experience, the W201 is considerably lighter and more "nimble" compared to the larger sedans. While some might argue that the W124 had advantages in "being a Mercedes" there is almost uniform agreement in the intial reviews of the W201 that it felt like a Mercedes. Peter Egan at Road & Track commented that after driving the 2.6L, the drivers side door of other cars seemed "tinny."