If you want to work your biceps, then do biceps exercises. Chin-ups of any sort are meant to be back exercises.
Andrew is right that the supinated (palms facing you) variation will allow the biceps to come more into play. However, it is still a back exercise and you should be feeling it in your back. Or, better yet, you should be using your back muscles for the exercise, not your arm muscles.
The above routine is fine if you’re looking to do an upper body routine (I’d personally add the standing biceps curl or another biceps curl variation for the biceps). You’ve basically got a vertical pull, vertical push, horizontal pull, horizontal push, and an isolation exercise for your biceps and triceps.
As far as the original question. There is no “better” way across the board. Behind the neck presses are a good exercise, but you rarely see people with the shoulder flexibility to do them full ROM. Notice the starting (bottom) position of the exercise in Mr. King’s recent article.
And beyond that it’s really just a matter of personal preference. I personally prefer either barbell shoulder presses to the front, or dumbbell shoulder presses. The former allows me to load up on the weight. While the latter allows me to get a similar ROM as in BTN presses without the shoulder strain.
But to each their own.