We eat occasionally at Nine Dragons. Pretty good food and service.
They can accomodate a larger group much easier than Chefs. If there is four in your party, then of course either will easily seat four.
But between the two, I would choose Chefs. But neither is shabby. Even with an ADR you may have a longer wait at Chef's. But of course everything will be super busy NYE.
Have a great time whatever you choose!