The problem with TransferWise from a business perspective is that the money appears on your bank statement to have come from a local bank account, of a party different from the party that is supposed to have paid your invoice. That's a dramatic difference for taxes & accounting from an international wire (charge VAT vs no VAT, being able to prove it).
Could you expand on that? Does that make a difference if I am just transferring money from an account abroad to another in the US for private use? Eg just moving money to from European account to my US account