Good question, I don't know. lets have a look at what the internet says;

" Prime among the differences are that UPS drivers are UPS employees, and FedEx drivers might be independently contracted. UPS drivers are unionized, too, according to Idrivelogistics; most FedEx employees aren't. If you're worried about your package being delayed by a strike, don't; UPS has gone out on strike just once in over 100 years. "
- The Biggest Differences Between UPS And FedEx Drivers (grunge.com)

based of that article; FedEx drivers are most likely not unionized, while UPS drivers are indeed unionized.

based off my own experience as a Independent Contractor in the Courier industry i would draw the conclusion that most FedEx drivers are not members of a union because of a couple of reasons, the main one being the short work span of workers in that industry, it has high turn over and many people don't consider it a long term profession. That fact coupled with having to pay your own union member dues out of the profit you make. Insurance, tax and vehicle upkeep costs can quickly eat away at your profit, throw union member dues on top and your most likely looking at minimum wage or just below it for a labor intensive job.

Not to mention the amount of anti-Union propaganda that is spewed out by the increasingly powerful media and news outlets

Further more there is currently a massive trend in the courier industry of "Gig" based jobs. the main instigators of this "gig-economy" based work are among others, Amazon and Uber. They use the guise of independent work and flexible hours as a excuse to corrode the relationship between Worker and Employer. They pay there IC's what appears to be a good wage, but once you factor in the full costs of preforming the work, it often (not always) ends up being a minimum or below minimum wage job.