Mason, that's a good question. I have only dug up large cherimoya trees to get rid of it so didn't need to worry about transplanting it.
But I have moved/transplated large loquats (4-6" diameter trunk), pluots, figs, and citrus. What I found is that if the tree you are trying to dig up for transplant has only a large/long taproot then it will be difficult to survive the move since you probably will end up cutting off the tap root. If it has many smaller roots or more roots besides the tap root then it should be good.
Since I will also be moving some fruit trees before summer, I should know how the large avocado tree (5"diameter trunk) and citrus (4"diameter citrus, 15yrs old) will do. Always good to try and leave as much of the dirt on the smaller roots if you can, but it can make the weight to much for you to carry out of the hole. Dig at least 1-1/2 ft away from the trunk around the tree, maybe 2ft deep. You should be able to see how much roots it has, if it only has the main tap root going down then it might not make it so leave it alone.