As I see it: Grammar, and pretty much nothing else.
I think what Stefan means is that there is no one method that has been improved on the most, because the 4x4x4 BLD event itself isn't very well developed in the first place. Besides, this isn't speedcubing, so there isn't a single method that solves the entire cube. People mix and match different methods for different "piece types" and find the best combination of methods that works for them, so you could have made your question clearer by asking which method is the best for each "piece type", but I think I've answered that question way earlier in this thread anyway (I hope).
If you really want an answer for your question, it's commutators, because that's the method that's been there since the start of big cubes BLD. But then again, there really isn't much to develop for commutators, except maybe find more algorithms, and that's why there's BH.