Ben Casey was a Bing Crosby Productions show while MGM produced Dr. Kildare and they weren't even broadcast on the same network. In fact I can't find a common theme other than the obvious medical settings, so the linkage is curious and I'm a little puzzled how Topps pulled it off. Each show ran from 1961 to 1966 and pulled decent ratings at first before fizzling out.
The Casey cards are a lot cripser in general appearance than the Kildares. Here's Ben with Dr. David Zorba (Sam Jaffe in real life), the Chief of Neurosurgery at County General. It's a rare pose, showing Vince Edwards with someone else in the frame: