It depends on context, and the situation in which you say it. English's a heavily context-dependent language.
The first is a statement of fact. That's what he did today.
A: "Did he get any exercise today?"
B: "Yes, he jogged in the park."
The second sounds like a lead-up to something more.
He was jogging in the park today. He usually just walks around.
Or an answer to a question.
A: "Have you seen him today?"
B: "Yes, he was jogging in the park."