You are correct. They have a very similar meaning with the usage you gave. "Roaring" and "Booming" are both verbs and onomatopoeias. In this case by saying "the economy is roaring" you are using it as a verb. To my knowledge, in the sentence "The economy is roaring" you are actually using the verb "roaring" in a way that "personifies" the economy since "the economy" is not a living thing. In this way, the phrases "the economy is booming" and "the economy is roaring" is a common figure of speech that English Speakers will use to refer to the current excellent state of the Economy.
Also, Patrick is correct. We often use the word "roar" to describe the sound of a lion or an animal that makes a similar noise.