If anything, I'd recommend working all sorts of grips (including neutral) and hand spacings. I prefer the neutral more than anything for a back pump, but if your goal is to work the biceps, I would focus more on the chin-ups. I know CrossFit is bordering blasphemy around here, but you might also want to look into 'kipping' during chins and pull-ups to help add to your dead hang numbers.
Pull-ups come in all sorts of grips and hand spacings; a chin-up is a pull-up with a palms-in grip. It's kind of like how a square is a type of rectangle but a rectangle is not a square.