Is there any difference between these sentences?
The hand that held the gun was dripping with sweat.
The hand that held the gun was dripping sweat.
The form “dripping with sweat” is perhaps more natural (ie, more likely to be said by a native speaker) than the other. However, if for some reason one needed to emphasize that drops of sweat were actually falling off (rather than just beading up or rolling down on the hand in question), one might use the second form.
The following form is stronger (less passive):
The hand that held the gun dripped with sweat.