FedEx is no saint, either. This had a $7000 acoustic in it; the box was dented, crushed, sopping wet and disintegrated till part of it was like a paper shopping bag, no paperwork or address label on it, if it hadn't been shipped with a second guitar it never would have arrived:
Fortunately, it was in a Hiscox case and the guitar was unscathed.
This one was not so lucky ... a $6000 acoustic, in a top-of-the-line Ameritage heavy duty case, in a double walled box absolutely stuffed with wadded up newspaper all around:
UPS is rumored to break more stuff, but easier on the claims. FedEx was an absolute bear to deal with, they finally paid but it was a big hassle. The first thing they will tell you is it's not their fault it got damaged because it wasn't packed correctly. They deny the claim and then you have to fight it out. They will deny it if the box has been shipped more than once, too.
My advice to you would be to pay to have either a FedEx/Kinkos or UPS Store pack the guitar and insure it fully. Then, if it gets broken, they can't lay it off on your substandard packing job because THEY packed it. And no matter how well it's packed, trust me, they can find a way to break it.
I have outside insurance for the guitars I ship, they pay right away, but with a $500 deductible.