"would a 38 super do good on a deer at around 60 yards" - No! Sorry!
The 38 Super, with the right loading, is adequate for smaller game like fallow or jungle deer, Javelina, Koti, small monkey, and people. It does not carry the power of a 357 magnum unless it is loaded to 1400'/sec+ with a 125 gn bullet and even then you can not expect it (the 9mm bullet) to perform on game as the tougher 357 slug does. That being said I have used the 38 Super, with a Col. Askins loading, to take Jaguar, but do not recommend it................
I would suggest the 357 for whitetail and the 38 Super for something else. JMHO. Mikey.