Limo Bus goes to the New Otani
In fact, the New Otani has direct bus service once or twice an hour from Narita. I find in unpleasantly large and quite mediocre, but have not stayed at the Hilton so can't compare it. I'd point out that, if one signs up online for the Okura Club International (no fee), some reasonable discounted rates become available. The Okura is, IMHO, quite superior to the New Otani.