UPS is Teamsters which means dealing with the union. The Teamsters have been trying to organize FedEx without much success. A few years ago I had a programmer working for me who was also working part time at FedEx. When faced with the decision of picking one or the other he went with FedEx. According to him Amazon was concerned about the union in UPS and were going to switch to FexEx but at least around here it never happened to any extend. I got a couple of FedEx deliveries but it mostly was the brown truck stopping in the driveway.
Amazon kicked FedEx to the curb last December to the point of telling the third party shippers not to use them. According to FedEx the Amazon contract wasn't a major part of their income but losing it didn't do much for FedEx stock.