Besides the two stated choices of copper and black pipe (steel) there is also high pressure propane hose.
Steve is correct that the line from the regulator back is low pressure, so the line doesn't have to be "super heavy duty".
However, there is/should be concern about vibration, flexing, and road debris contacting the propane line if it is exposed.
Flexible copper line is favored because of the ability to bend it around obstacles without the need to cut and add fittings as is required with black pipe.
While a good system properly installed doesn't leak, the more joints you have, the better the chances of a leak.
There are a couple low cost methods for protecting the soft copper pipe; one is to weld a steel tube under the trailer, and run it through.
The most common is to slide it through a length of garden hose (before flaring and bending) the tubing can still be shaped with the flexible hose covering.
In the end, it really doesn't matter what you use, as long as road debris won't damage it, and there are no leaks
I used copper for the long run from front to rear, because my frame setup would not allow a single straight run of black pipe (my first choice).
At each end, I used high pressure LP hose, flexible, and very strong, able to withstand any flexing and chafing as it went through the floor.
(The hose WAS NOT cheap rubber, it was very expensive 1200psi steel braided line designed for only for LPG high pressure systems.
A specialty shop cut the line and installed the ends with the proper equipment, no hose clamps here...
Rubber hose, gas line, and hydraulic hose are not designed for LPG. and will fail.)
The high psi rating was not needed for the very low pressure side of the system it was being used on, but because of its construction, it is stronger than any other product on the market that is flexible.)
I also favor it for the ability to go from below the floor to my cook stove with no joints to potentially leak, and because it is so flexible, I made the line extra long so I can easily pick up my stove (while connected) and move it around the counter for easy cleaning (can't do that too many times with soft copper...)