They are both correct and natural. A native speaker would choose on the basis of what was said before, and what will be said next, and what they want to emphasize. For example, if you asked me "Have you ever been to Tokyo," I would be likely to answer "I once went to Tokyo on business, but I didn't get to see any tourist attractions." If you asked me "Were you away on a trip," I would be likely to answer "Yes, I went on a business trip to Tokyo."

Both expressions are grammatically correct and commonly used, but the choice between them may depend on personal preference or the context in which you're communicating. Here's a breakdown: "I went to Tokyo on business." This expression is concise and straightforward. It directly states the purpose of the trip (business) and the destination (Tokyo). It's suitable for casual conversation or when brevity is preferred. "I went on a business trip to Tokyo." This expression provides a bit more detail by explicitly mentioning that the trip was for business and specifying it as a "business trip." It's slightly more formal and may be preferred in professional settings or when you want to emphasize the purpose of the trip. Ultimately, both expressions convey the same meaning, so you can choose the one that feels most natural to you or fits the context in which you're communicating.