It's been a while since I shipped a bike or frame, but FedEx was always substantially cheaper when I compared with UPS or USPS. For example, I shipped a complete bike to the Chicago area when I flew up there to ride a bike tour with my brother. FedEx charged me less than $40 to ship from Raleigh, NC, to Geneva, IL. My brother shipped the bike back to me using USPS because FedEx didn't have a location in his town, and they charged about $100 for the exact same package. To add insult to injury, the top of the box was smashed in when the bike arrived, and my frame would have been badly dented if I hadn't don't such a careful job packing the bike.

Another time I shipped a frame and fork from Raleigh to Portland or Seattle for about $35 using FedEx, and it would have cost more than $100 using USPS.