For all flat work (at least in stock breed shows - AQHA, APHA, Apps, etc), you want them to be long and low, so both HUS and Hack on the rail. The slowness comes from a slow cadence. The horses are covering a huge amount of ground, but it's all with the length of stride with a slow cadence.
Over the fences for Hunter Hack, you would jump them just like you would in any Working Hunter class. 12' stride down the line, quiet, and meeting the fences easily. It's common to see a little elevation of head set, but still on the bit, and definitely not up and in your face.
Hope this helps. let me know if you have any other questions.