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.

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.