I had a hunch Noel would be the one disparaging Sondheim; he'd be inconsistant if he didn't.
What ties Sondheim to Hammerstein, and not to Hart, isn't the mentor/student relationship they had. It has more to do with writing for character, which was a trait of Hammerstein's. Hart's lyrics are generalized, not set for any particular characters. Hammerstein, on the other hand, wrote for the characters in his plays (let's not forget that he is also one of the greatest bookwriters the musical has ever known).
The King and I, in particular, is filled with character songs, pieces that could not be sung by any other character in that show. Anna's songs ("I Whistle a Happy Tune," "Getting to Know You," "Shall We Dance" and particularly "Hello, Young Lovers") are all consistant in their point of view, that of a woman who has known sadness yet refuses to desert her basic optimism. She could never have sung "Something Wonderful," which is rightfully Lady Thiang's song, explaining a relationship Anna has yet to understand. Similarly, "My Lord and Master" and "We Kiss in a Shadow" belong to Tuptim; the emotions in those songs are not those felt by any of the other characters.
Sondheim carries this connection to character even further. In Anyone Can Whistle, the title song is clearly Fay's; no one else is in that quandry of being unable to connect. "Everybody Says Don't" is in turn clearly Hapgood's song, even while it resonates with Fay's earlier melody. And both are filled with emotion, not a lack of same.
Let's jump ahead to much later in Sondheim's career, to Assassins. This is not some simple history lesson; this is a probing into the hearts of people we've previously been taught to regard as cardboard villians. The slow waltz that Czolgosz sings at the beginning and end of "The Gun Song" reveal his passionate hatred for the toll the mechanization has taken on society; this is hardly heartless, he sings from his heart. Similarly, Booth's plea to make his motives understood in "The Ballad of Booth" is filled with passion, a passionate love for his country. It isn't until he calls Lincoln a "nigger-lover" that we are reminded of the foulness in his soul; until that repellant moment, the audience falls into his own rapture. Even in as simple a song as "Unworthy of Your Love," Sondheim fills his characters with passion and heart, even when those passions are pointed in negative directions.
Jumping again to an earlier show, what is Sweeney Todd's "Epiphany" but the baring of a soul right down to the heart, showing all the bitterness, anger, and sense of loss that the man has.
Sondheim has as much heart, and as much empathy for his characters, as Hammerstein ever had.
