Elaborate and explain the differences between their views? It seems like u are just quoting direct w/o explaining or referring to je rinpoche's works that i do not even know what are the differences between the views.
I am not able to, not sure about you,swallow Lama Tsong Khapa's (from here on I'll use the abrrevation LTKP) interpretation of Madhyamika once you understand it.
One of the point that stands out, which I think is at odd (and thus not able to swallow) with the entire established Buddhist doctrine according to traditional Indian sources. It is regarding the point that not all concepts have to be discarded in order to attain enlightenment (aka direct experience of emptiness). In LTKP's view, his particular method of negating truth (negating truth or mental concepts such as existence, non existence, both or not both is the main subject of treatment of Madhyamika) is the Ultimate truth (though it is still a mental concept) is not to be negated
. To LTKP, that very methodology deployed to negate all other truths IS the ultimate truth and is not to be negated. However, the traditional ( which traditional Indian sources such as Sutras, texts of Nargajuna, Chandrakirti etc..) view which Gorampa
was defending holds that ALL concepts
including those method delineated by Madhyamika need also to be discarded or negated
in order to attain the true Ultimate view. In other word, LTKP held that the logical reasoning in Madhyamika and particularly his unique interpretation is the Ultimate truth and should not be negated wheareas Gorampa held that the logical reasoning presented in Madhyamika is merely a nominal truth which ordinary beings can use to negate mental concepts (or proliferation is also the word used or "negate the four extremes") but ultimately has to be also discarded in order to experience the ultimate truth.
Another point is that LTKP adhered to the logic (familiar in western philosophy and has a name which I can't remember) that negative of a negative should be affirmative. For example, proving that something is not nonexistence amount to affirming that something is existing. Thus he sees the Madhyamika logical framework of refuting all four extremes (i.e. existing, non existing, both or not both) to be illogical without further qualification. On the other hand, to Gorampa, the four extremes (existing, non existing, both or not both) are all possible concepts that a ordinary beings can possibly construe on any object. Thus negating all four extremes is not self contradictory in logic but simply means that the ultimate truth is beyond all conceptualisation.
Of course there are many more differences and they are not trivial because it will influence how one practices and has other implications. maybe, these can be written in another post.
For a concise study of Gorampa interpretation of Madhyamika and polemics against LTKP, and if you do not wish to read the entire book "Freedom from extremes: Gorampa's "Distinguishing the views" and the polemics of emptiness", you may readhttp://plato.stanford.edu/entries/gorampa/