Rotation properties and methods of a mesh are set to be about an axis through the local origin of a mesh. In this case all that is necessary is to define an axis is a vector.
The rotate method has the following form where axis is a vector of the type (x, y, z), angle is in radians and space is local (BABYLON.Space.LOCAL) or world (BABYLON.Space.WORLD)
mesh.rotate(axis, angle, space);
Using rotate is cumulative, that is the rotation angle is added to the current rotation angle, so in an animation the same angle is used in each frame.
Read more about rotate
Just as you set mesh.rotation to a 3 dimensional vector you set mesh.rotationQuaternion to a quaternion, a 4 dimensional vector (x, y, z, w) where x, y, z defines a world axis and w the angle of rotation about the axis.
You set the rotationQuaternion property given an axis and an angle by creating a quaternion as follows
mesh.rotationQuaternion = new BABYLON.Quaternion.RotationAxis(axis, angle);
As for rotation a further use of rotationQuaternion re-sets the rotation to the new angle, so in an animation the angle of rotation is increased each frame.