Well, I can't make up for missing Terence Malick's The New World, but I just got back from a screening of Days of Heaven, which I had not seen before.
In a word: the film is an unforgettable, truly a one-of-a-kind experience: Malick is a director who knows intuitively that cinema is a medium of the moving image, and not simply a medium for filming scripts (Antonioni, one suspects, would have been proud, given the number of film directors who simply appear to "translate" texts onto the screen).
The film has a timeless, magical quality about it, involving some of the most stunning images I have ever seen on screen, combined with a Biblical cadence that is anything but inadvertent. Not to mention that it serves as an implicit critique of the American (but perhaps not only American) myth -- most forcefully articulated in the Western -- that one's pasts may be fled, and left behind for good in some fashion.
The only other film of Malick's that I have seen is A Thin Red Line, but the man would be a master had he never done anything except for Days of Heaven...