Well, we can use both phrases to communicate the same thing. In other words they express the same thing IN THE EXAMPLE. BUT Grammatically they are different, in the sense that 'being' is a temporary thing. It means "what I say at the moment OR in a past period of time that continues until the present and will continue into the future " (the exact period of time is not specified). 'to be' means that it's a permanent quality. We can use this in the sense that the speaker (the subject of the sentence) believes that their opinion is permanent/fixed. IF we want to highlight the temporary aspect we choose 'being' ..."I was joking previously, but now I am being serious." REMEMBER that "I am serious." can also be used to describe a personal quality ... that's a different context to your example

"I am serious" is more a statement about yourself. It is less a statement about what you are doing or saying at any particular moment. "I am being serious" is a statement more about the way you are acting or speaking at a particular moment. It describes less what sort of person you are.