There are several reasons why political speeches and persuasive writing are similar. One of the reasons is the objective. Both types of writing try to put a claim forward and convince people of the validity of this statement. Therefore, both types of writing can be considered persuasive.
The second reason is the fact that political speeches and persuasive writing use some of the same rhetorical devices. For example, both types of texts use pathos, logos and ethos in order to provide support for their claims and persuade the audience of a particular position.