No, not yet. As I said, the boys are fairly young in the story; while their relationship is an integral part, it's just as much mentor!Snape. It's mostly about Harry bonding with a basilisk and the fallout of that in general.

AS an impression, I'd say that initially Draco's personality is a bit more assertive (quite logical, given how the boys were in canon during books 3 and 4), but Harry is developing his own brand of self-confidence and gradually learns to stand his own ground. There's also some Dumbledore-bashing.