Most are half scale, but the two exceptions are 1/4 scale and 80% scale. A couple of the older mobile replicas have been retired and installed as permanent displays. One of these, the Dignity Memorial Vietnam Wall, was installed at Ft. Benning, GA this year as a 5-year "permanent" display. There's another half scale permanent display in Pensacola and I've seen a reference to one in Kansas but I haven't confirmed that.
Besides the Moving Wall referenced in the OP the other mobile replicas are:
The Wall That Heals Traveling Wall (half scale) (includes mobile museum)
Vietnam Veterans Memorial Fund
http://www.vvmf.org/twth
Bringing Home the Wall Memorial (1/4 scale)
Tom Twigg and his wife, Dee, built it in the 1990s and started traveling around the country. The current version has been downsized from the original half scale one to permit indoor display at places like church halls and VA hospitals.
http://www.bringinghomethewall.com/media/new_memorial_wall.html
The Vietnam Traveling Memorial Wall (3/5 scale)
Vietnam and All Veterans of Brevard
The Vietnam Traveling Memorial Wall® is part of the Vietnam and All Veterans of Brevard (V V B) located in Brevard County Florida. (Melbourne, FL)
http://www.travelingwall.us/
The American Veterans Traveling Tribute Wall (80 percent scale)
AVTT
It is 360 feet long, 8 feet high.
http://www.avtt.org/resources/Sponsor-Area/Sponsor-Only-Area/Traveling-Wall-Informational-Handout.pdf
The Mobile Vietnam Veterans Memorial for the Antelope Valley (AV Wall) (half scale)
Point Man Antelope Valley (California)
The 'AV Wall' is the only one of the mobile replicas that does not travel around the country. It was created for periodic display locally, though it has traveled several times to other display sites in California. It was last displayed in Simi, CA over Memorial Day 2014 and will celebrate its 5th anniversary with a display in Palmdale, CA over Veterans Day.
http://www.avwall.org/