Blew up is perhaps a little more colloquial. Erupted is slightly more formal. In English we have many verbs that can be a verb plus a preposition or a verb without a preposition. For example he came in. He entered. He put up with a lot. He tolerated a lot. If you research the subject you would find that most of these differences go back to 1066 when the Normans invaded England. French became the language of the government, the church and the army. So frequently we have words that have an English (Germanic) origin and we have words that have a French origin. Ordinarily the French equivalent is considered a little more literary.

The question should be is there a difference between the two of them. I do not think that there is any significant difference between the two expressions. They both convey that the person reacted with uncontrolled anger.

Both are good.

He blew up seems more literal as if he is literally exploding like a bomb, but erupting with anger is more figurative to convey his intense emotion which should be used in this context