Obviously, the vector is the one without the awkward white box around it. Also, notice how the artist has placed a white outline around the vector image. You can request this if placing on a dark background to make the image show up better. Its all part of the service!
If you need something with about as much detail vectorized, you should always get a quote and opinion first before proceeding.
You can upload a quote for a speedy and efficient process here: Here (no account required).