I just had a handgun shipped to me in Maine and learned a lot. UPS stores are franchises and can have their own rules & regs regarding the shipping of firearms, and most don't due to liability issues. That said, you can mail a firearm (handgun or long gun) through UPS, but you have to go to a UPS Customer Service Hub to do it.
One of the downers about both UPS & FedEx, is that they may ask you to see a copy of the FFL to verify the shipping address. They both say this on their websites, and will likely refuse to ship it if you cannot produce a FFL with the same shipping address if you're asked. FFL holders can ship handguns to other FFL holders via USPS, but they have to fill out a form and file it with their local post office.
I thought I was saving money because I have an friend with an FFL, and he doesn't charge me for transfers and such, instead he makes me do all the paperwork (mine & his) as well as call it in. The handgun mentioned above came from Nebrask so I had the guy mail it overnight to my friend via UPS with insurance. Cost $69. Turns out that the local gunshop there in NE would have done it for $60 which was cheaper than the $69 I paid. Moral of the story - It's cheaper for FFL's to send to each other through USPS, so find one and build a really good working relationship. :-)