I used to not ever have issue with Fedex. That has changed!
I have shipped ammo Fedex in the past by packing, labeling with ORMD and dropping off at the hub (7 minutes from home). Recently, I took a trip out to WY for prairie dogs and needed to ship a lot of ammo. I packed it, labeled it and took it to the hub. The package was refused and I was told the only way I could get it shipped was to go home, access my account online, get a label and schedule a pickup. I spoke to Fedex corporate about it and they confirmed that is the way they want it done. They are also starting to hassle me about shipping firearms lately.
As for handguns, I have a bud with an FFL and he can ship them USPS. It is a lot cheaper than overnight UPS or Fedex.
Lastly, I have not used UPS in years. They really suck! They lost an entire plane load of packages in a crash while trying to land at Bham airport and now they have had a disgruntled employee workplace shooting at one of the two local hubs. Not a happy place.