How to repair this kitchen drawer front panel?
Metal corner braces will work to some degree, but will be hideous. I recently rebuilt one in my home that had been repaired that way. You'll see them every time you open the drawer, along with the torn-out face of the panels. 

I would cut a new board (solid wood, plywood, particle board) exactly the size of the inner dimensions of the drawer, and mount it to the back side of the drawer front using countersunk flathead screws and glue. This will then slide into the drawer when the front is put in place, giving you solid mounting and covering the damaged surfaces. 

Carefully pilot and countersink flathead screws from the sides and bottom of the drawer to attach the drawer front via this new board. Glue would be a good idea here, too. 

Plan view:

 |  |                 |  |
 |  |                 |  |
 |  |     new block   |  |
 |  |        |        |  |
 |  | ________________|  |
 |__||_______________||__|
|_________________________|
             |
             |
        drawer front