What is OFF?

Object File Format, and about as plain as a mesh can get: a count of vertices and faces, then the vertices and faces. It comes out of academic geometry work, where nobody wanted to parse anything more complicated to test an algorithm.

What is OBJ?

Wavefront OBJ is plain text, thirty-five years old, and readable by every 3D application in existence. Vertices, faces, texture coordinates and named groups, with materials kept in a separate .mtl file alongside - which is the part that most often goes missing when a model is shared.