Yes, skinnier nails (box nails) are less likely to split the wood than the thicker (common nails). However, most of the construction joints load the fastener in a shear direction so the larger the cross sectional area the less likely for joint failure. For withdrawal, the screws are far superior, just don't use drywall screws to hold anything other than drywall, their heads are designed so they can be broken off and taped over if need be so they're not nearly as strong as regular construction screws.