The similarity is that persuasive speeches and persuasive essays share some common features like : Subjectivity,5 paragraphs( introdution,body ( 3 paragraphs or more ) and a conclusion. The difference is that when delivering a persuasive speech we use many elements to convey the meaning of the speech by using gestures,non-verbal communication.
The similarity is quite obvious. It would be that both of them are trying to persuade someone to think how you do or do what you are doing. They both should have an audience and they should both have the same structure, as well as a good amount of information to prove your point. The differences would be that an essay is not verbal like a speech and an requires more gestures to connect and persuade. With a speech you also rely on your posture, the way you convey yourself, etc, while in an essay, you rely only on what you have written down.