Having sailed on the Pineapple Run with Matson and dealt with the autos I can add to this.
First off, for any company, Longshoreman DO NOT care about your car... The longshoremen drive like madmen through the decks of the ship. The Lurline was half container/half auto. I have seen several of them almost get into accidents from flying around the corners.(A lot of cars leave through the port of Richmond if in NoCal, or Long Beach in SoCal, so you can imagine the quality of people.) If the load boss is good the drivers stay in check.
Depending on what you pay for is where your car goes with Matson... cheapest and you are left out on one of the open air decks, pay more and you go into the hold or a container. If its the winter or a good storm comes through your car will get blasted by a wave if on a lower deck which is open air. If the Chief Mate is good the ABs will give the cars a good rinse.
Containers offer more protection, but as always there still are problems, I have seen containers dropped, tipped over, and on fire. (none were cars though)
Pasha has taken a good chunk of money away from Matson, they have a relatively new dedicated Ro/Ro which runs through the Islands and the west coast. I have seen pics of the decks and operations from friends who were on it.
http://www.pashahawaii.com/index.php?s=sailserv&a=0098/
Horizon is Matson's main competition for shipping cargo to Hawaii. They don't have any auto ships, so all they transport their cars in are containers.
For the most part, pretty much all of the cars that went through the ship, pretty much all left with no damage to them.
A few random items: If you have a nice car, the crew will sit in it during transit..... the Shelby Cobra was nice.
We could always park your car next to the Nuclear waste container, or have it dented by a Bull which escaped from the cattle trailers (I wish I had the video for this, it happened in the 90s and ended up in the Engine Room)