To me, as Randolf and Martin have pointed out in their answers, there is a slight difference in the timeframe. "No supo la respuesta" sounds to me like "no supo qué responder en ese momento".
So for example, about an exam, you could say, "me preguntaron X, y no supe la respuesta". It doesn't mean I didn't have the knowledge, but I was unable to give a correct answer at that moment.
Also, if instead of "la respuesta" you use "qué responder", as in "no supe qué responder", it can mean or sound like "I didn't answer because I had no valid or convincing answer". For example: "cuando mi madre me preguntó cómo se había roto el jarrón chino, no supe qué responder" (of course, I knew I had been using it as a basket to play basketball, but that would not be convincing enough).