Large amounts to you may not be large to the banks. They maintain foreign currency exchange as a product they offer to customers and hence need to make money off that service. You will never ever get the rates you see online as those would be the rates the banks get.

If you have a brokerage account, they can treat the exchange as a trade and work to get your the best rate but on top of that you'd be paying commission so net net it may be a wash.