Assail is more commonly used to describe the action of launching a verbal attack but does not exclude a physical attack, whereas assault is more commonly used in a physical attack but does not exclude a verbal attack. However, attack amounting to an assault per se in civil law (Common Law) may constitute the mere threat of a battery (physical assault) so that, for example, when someone shakes his fist at an intended victim and motions menacingly towards him, the inchoate action alone constitutes a civil assault (but not a criminal assault), even where the intended victim of the threatened civil law battery (physical attack) manages to run out of harm's way.
Assail:
to attack someone violently or criticize someone strongly (emphasis added) -- Cambridge Dictionary
Assault:
1). The definition of an assault is an act that causes verbal or physical (emphasis added) injury -- (yourdictionary.com)
2). (Law) An act that threatens physical harm to a person, whether or not actual harm is done -- (yourdictionary.com)