You would use cozy to describe an environment or space, such as a room or cafe shop. You would use comfy to describe an object such as a couch, wool jacket, or teddy bear.

They can be used interchangeably at most times, however, "comfy" is less formal because it is just a short way of saying "comfortable." [Cozy] - 1. Giving a feeling of comfort, warmth, and relaxation. "Your home is very cozy." [Comfy] - 1.   Giving comfort or physical relief.... AND 2. At ease. "Wearing this sweater makes me feel so comfy."