설득하다 : It contains meaning to persuade someone who doesn't agree with your idea or opinion.
납득하다 close to "understanding or accept".
but "~~시키다" means making someone do something, so I think it's pretty similar as long as you use "설득하다, 납득하다" with "시키다", you can think like..
"넌 나를 설득시켰어-You persuade me" --> At first, I didn't agree with your idea, but you explained to me why I have to agree, so now I agree with and believe your idea.
"넌 나를 납득시켰어 - At first, I couldn't accept your idea. But you explained it to me so now I can understand and accept your idea.