If you designed your model with Art of Illusion, you should pay attention to the value in the Max Surface Error field when you select Export > Wavefront menu item:



This value is used to approximate round surfaces to triangles and rectangles that are the only shapes supported by OBJ format. If you use a too small value (like you probably did), this will end up to the creation many super small triangles in a big OBJ file, with no visual benefit.
Try a bigger value until you get a correct result with smooth enough surfaces.