A good rule of thumb is to use a fastener based on the direction it will be loaded. Screws are very strong at resisting forces parallel to their shaft (i.e. pull-out resistance) but are weak at resisting forces perpendicular to their shaft (i.e. shear strength). Nails, conversely, are less strong parallel, but are vastly superior at resisting forces perpendicular to their shaft. That's why you use nails for framing and screws for drywall. The kicker with drywall is that in vertical applications (i.e. walls) it needs to resist parallel and perpendicular forces, but most pros still use drywall screws despite the lower shear strength presumably due to ease of installation. So in the case of flooring underlayment there is virtually no need for pull-out resistance as gravity takes care of that for you, and a significant need for shear strength as foot falls still carry a large amount of force along the surface of the flooring (i.e. shear strength).

