High volume Merchant Fulfilled- Shipping carriers

We have been using DHL eCommerce and UPS SurePost for our merchant fulfilled orders. I noticed Amazon has through Buy Shipping rates with USPS Ground Advantage and USPS Ground Advantage Cubic. Has anyone been using this carrier, either through their own rates or via Amazon’s? What has your experience been?

What are you finding is the cheapest/best way to ship merchant fulfilled orders nowadays?

Volume would be 100-500 pieces per day.