I would argue that the two phrases have mostly the same meaning.
That said, I would say that "down pat" more implies something memorized as rote, and would not be used with a more abstract thing, where just "down" might be.
"I've got the Declaration of Independence down pat." — fine.
"I've got the Declaration of Independence down." — fine, if a little odd.
"I've got the General Theory of Relativity down." — fine.
"I've got the General Theory of Relativity down pat." — quite weird
Also, I might argue that "down" without the "pat" might be more forceful than with. I've used it to mean a full and complete understanding, where as something that is "down pat" is merely memorized.