I trust airlines more than UPS or FED-EX...but that's just me. I want my bow in my hand till the last second, then back in my hand asap. I think it's actually handled less than if going through shipping and the short time period means less odds of problems, imho.
If you do have to ship, go with Fedex, they will let you insure for what something is worth, UPS has a max limit under what most top end bows cost (though they don't tell you that directly). They also have an insurance payout percentage for damaged goods somewhere around 30%...typically they blame packaging.