From all the pictures that I can find, the '32 & '33 Studebaker were the only years that had the oval shaped headlights. The '32 grille was more vertical while the '33 sloped back. '34 & '35 had a sloped grille like the '33, but had round headlights and the front fenders were more rounded and didn't have the small running lights... This is only on the big luxury models (President?). The Rockne models are smaller and have round headlights and a grille more akin to a Packard.

I'm no expert on Studebakers; I'm just going by pictures I have found. There may be a Stude enthusiast out there that can tell us more.