It's not the carrier, it's the driver and the staff who handle the package. Most don't care a toss and will, er, toss your bike around no matter how many "Fragile" signs are stuck on it. Many courier companies act as agents for TNT, who did this to a bike I sold by driving something through the carton:
In this case I had a struggle getting anything out of TNT because the buyer's idiot wife signed for the goods in "good condition" despite the carton being badly crushed and a huge hole right through it. Do not allow the delivery driver to harrass you; get the package inside and inspect it carefully and if you have the slightest doubt, sign for it as "damaged".
You'll be pleased to know that by getting the TNT rep to come to our office (I sent it through my employer's account) and by refusing to accept their first derisory offer I managed to get about half the cost of the repair out of TNT.
I've used Paisley Freight since then to carry bikes and wheels but they just use TNT as their carrier.
I think that picture may have just made my mind up.
Plus fuel prices are dropping.
I'll get my car keys...