Also for record, my dm disallowed monks unarmored defense, but allowed barbarian unarmored defense.
Why disallow one but not the other? Barbarian allows shield use (applicable when not in animal form), and while a cursory glance at the various beasts shows that con+dex is as common as wis+dex in giving a 13ish AC, I suspect that con+dex might give a slight advantage.
PHB 67 said:You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
Why disallow one but not the other? Barbarian allows shield use (applicable when not in animal form), and while a cursory glance at the various beasts shows that con+dex is as common as wis+dex in giving a 13ish AC, I suspect that con+dex might give a slight advantage.
Assuming you increase your WIS as you level the Monk version is as good as the best possible Barbarian wild shape AC and usually better.