First, Gavin, thanks for taking the barb well.  I'm bad for those. 
Now as for the Quartets, I still can't see how TWL trumps them.  TWL may be the best modernist poem but the 4Q is a poem that finds the heart of light in the darkness that is the 20th century.  In that way yes, Eliot is _very_ much a poet of the 20th century, as Milton is very much 17th century.  I also don't see the self-referentiation of 4Q -- every line seems pulled from something Eliot read, the ultimate palimpsest on which to rebuild ourselves.
Now, for the elucidation:
In _Samson Agonistes_, a closet (never meant to be produced) play, Milton was trying to destroy English Tragedy.  As far as he was concerned, because of the redemption offered by Christ, we never needed tragedies to watch anyway (at least after 30 A.D. or so).  This is why SA ends with the redemptive suicide of Samson.  Even if it's sad, Milton shows us, Samson still lives on in the end so "ha ha Shakespeare, we don't need you." Now, Milton _needed_ to do this because he was constantly defining himself against Shakespeare (if I had the time to paw through my Riverside Milton I'd find that part of one of the essays).   Eliot has to brush up against two Bloomian Pops, Dante and Milton.  Although I said that Eliot was essentially done with Durante by the time of 4Q, that's slightly inaccurate.  Milton, however, is FAR more important to the poem than Dante, Dante provides structure and Milton is the gravity that Eliot is working against to write the poem.

Now, Eliot writes MitC because he thinks "ha ha Milton, we do need tragedy, even if it is redemptive" because well, he lived through Hell 1 and Hell 2.

More later, must tutor Taiwanese boy now.