FAQ

    The only recommendations I could find about transplanting Joshua trees are for Arizona, so just move up the dates (our growing season is much shorter here than there). Take a look:
http://www.arizonacactussales.com/tips/joshua.htm
   I know Joshua trees can survive here in the Salt Lake Valley, but try to avoid low areas where cold air can pool - those are frost pockets.   The root system you dig up to transplant will be fairly shallow. You must support the trees with stakes at least one year so that they won't fall over.

The smaller plant has a better chance at surviving, since the tall plant will have much higher water demands and relatively fewer roots. Be sure to give the plants extra irrigation this fall and next spring until the root systems can regenerate. But, don't keep the soil too moist or the roots will rot.