Fed Ex:
Requires a box check. You send them a sample box, packed exactly the way it would be if you were shipping a reptile. They approve it, then you fill out some paperwork and get a shipping waiver. (That's the way it's supposed to work--I haven't got my waiver yet, but that's another story).
Delta:
Requires a facility check. You will have to pay a small fee, and someone will come out and inspect your reptile facility/room. If all is well, they will approve you to ship reptiles using their service.
Fed Ex's prices are lower than Delta's for small animals and small orders. Delta Dash can be more economical for large animals, or large number of animals that take up more space (IE, larger packages).
Fed Ex will only deliver reptiles business to business. If you don't have a business address to ship to, it would be wise to send the package to the Fed Ex hub close to your buyer, and have it held there for pickup.
Delta ships airport to airport--you drop the animals off at your airport, and your buyer picks them up at their airport.