In contemporary English, the difference between revive and revivify is generally that revivify is unlikely to be used for people or animals. For events, activities, organizations, and so forth, revive and revivify are very close synonyms.
Cambridge Dictionary's definition for revivify:
to give new energy and strength to an event or activity:
A leader with real charisma is needed to revivify the political party. (boldface mine)
To revivify a situation, event, or activity means to make it more active, lively, or efficient. (boldface mine)
According to the OED, when it first came into English, it could be applied to people or animals. And it is still used for the sense of bringing corpses back to life.
transitive. To reanimate or restore to life. Also: to raise from the dead or from the grave.
1883 H. Drummond Nat. Law in Spiritual World The biologist cannot devitalise a plant or an animal and revivify it again.
1921 Jrnl. Soc. Oriental Res. The kings, the offspring of the gods, were destined to die, to be revivified, and to live in heaven.
2001 M. W. Dickie Magic & Magicians in Greco-Roman World Public displays consist in healing the lame, curing blindness and revivifying corpses.
Except for bringing corpses back to life, none of the OED's citations since 1900 is used for animals or people.