FedEx is definitely among the worst.
Twice in the past year or so I've had a large-ish packages arrive that required a signature. FedEx left a note and required that I go to their office (about 20 minutes away) to pick up the package. There was no option to schedule re-delivery for a time that I'd be home (without paying extra) or to sign to let them leave it at the front door or with a neighbor (I work during the day, like most of us). UPS in comparison has multiple pickup places within minutes of my house, and never has a problem leaving a signature-required package with a neighbor or on the front door if I sign the notice for them (and sometimes even if I don't...).
Another fun experience with FedEx, though this was over 10 years ago (I feel old saying that ...) I had ordered a bunch of parts for a new computer. Tracking number showed that it was delivered and left with the super (I was living in an apt building at the time). That normally would be fine and normal behavior. Except for the fact that they left it with the super of the WRONG BUILDING. Two weeks later, getting nowhere with either the retailer or FedEx's claim process, my package magically showed up on the door (and yes, the address was correct on the box). I was lucky that the super from a block away was a nice, honest guy otherwise I would've been out a lot of money (and this was back when I was still in HS).
USPS isn't perfect either ... or at least my postman lacks common sense. They love sticking small-ish packages in the regular mailbox (I don't blame them...it's closer than the dedicated package box). The problem is that they ALWAYS try sticking it in the mailbox first. Even if it requires stuffing the rest of my mail into a messy ball. Even if the package just barely fits into the box from the postman's side. On occassion I've had to wait several days to get my package because it wouldn't fit out the front, and it took several days of pulling out all other mail and replacing with a sticky note before the postman realized that the package was stuck and removed it for me. On several other occasions I've actually resorted to cutting the box open inside the mailbox so that I could get the contents out without waiting...
I guess USPS and FedEx have annoyed me more than I thought given how much I just wrote . . .