As used, potent and powerful are fairly close synonyms in these instances. The meanings would be largely the same with only some nuanced difference in emphasis that few people would likely notice. I find potent to be a stronger adjective than powerful in these uses only because in other contexts powerful can mean other things such as authoritative, or formidable, which make it a more general adje
They have a similar meaning, but there is a subtle shade of nuance - rooted in euphony, rhythm, emphasis, tradition, and idiom - so that they are typically used differently, and are not interchangeable. In the examples you gave, "potent" is typically not used - and the phrase "powerful argument" is infrequently heard. In any case, the word "potent" is not often heard. Some examples of usage: