What does a Lexus RX has which any other similar car from Toyota such as the Matrix does not have? I know that the RX is miles ahead in luxury but when we compare the features - does one really feel the difference in the RX?

For example the Matrix does not have:

Leather
GPS navigation (as of 2004 and later)
V6 engine
Mark Levinson Stereo System
Power Tailgate

Just drive a Matrix and an RX back to back and you'll notice a world of a difference.

YOU BET you do! It handles much better, visibility is better, it's easier to load (because of the automatic rear door), and is much more comfortable to be in.
Yay, Lexus!