I have moved my horse across the United States three times, from Colorado to Massachusetts, then four years later from Mass to Colorado, and a year and a half later, from Colorado to New York so she could get on a plane and fly to the UK (well, to Amsterdam and then got on a lorry to go to England).
I had a trailer but went with the commercial shipping company because they have experience with transporting horses huge distances, whereas I don't. I hauled the trailer to Mass and back with a bike in the back. :) Shipping companies have stables where they lay over, whereas you'd have to find that on your own. Your horse also gets company for his long trip. The shipping company I used to move her from CO to MA and back was called All-State. The horse handling seemed fine but they transported the horses in an eight horse slant load, so it wasn't exactly luxury accommodation. It was relatively cheap though -- about $900.
When she had to go to JFK, the company dealing with the international shipping contracted with a domestic shipping company called Blue Chip, and these guys were awesome. They used to huge air ride truck, a far more comfortable ride than a trailer. My horse was reluctant to get on the lorry and the driver, who knew his horsemanship, did an excellent job convincing her that she wanted to go up that ramp. I'd definitely recommend those guys.
I can't remember exactly how long it took to go from CO to MA and back. Probably in the range four to six days. The UK trip was a total of 10 days to two weeks but she had a couple days layover in a barn in New York, a night in Amsterdam, a couple days at a barn in Kent, and a night in Newmarket. I reckon the US leg of the trip was five or six days.
It is undoubtedly stressful for them. The vast majority of horses I know who have done long distance travel drop a few pounds, but otherwise they are fine. They recover pretty quickly and put the weight back on.