Paging the expert on such horticultural things...
WTW, maybe you can help...
Here's some general advice, even though I'm not in your zone and don't know either tree type very well...
1. I take it this is more of a "switch" than a tree in appearance...probably a 2yr old seedling or cutting? You don't mention how tall it is, but under good conditions you'll likely see branching begin after the first full year in the ground. Rule of thumb for new woody shrubs and trees is: the first year it sleeps, the second year it creeps, the third year it leaps! In other words, it has to esablish a good root system before you'll see much top growth, so don't lose patience...once the roots are in and it's acclimated it'll start making visible progress and at some point the third year it'll really take off.
Keep it watered, mulched and if you feed it use either root stimulator or nothing more than 1/2 dose of an all-purpose fertilizer (like Miracle-Gro), since you don't want to stimulate more top-growth than the roots can support right now. I prefer water-soluble fertilizers because the pound-in-tree-stakes don't always disperse reliably, and with such a small area of feeder roots right now you need to be sure the nutrients are readily available.
2. Don't prune anything until well after the last freeze, after bud-break and the new leaves appear. What looks dead now may still have life. I'm not familiar with this fig, but from what I've found online it's winter-hardy in Phoenix except for newly planted trees, which may have leaf-drop. Even if you're north of Phoenix, if it's planted with a southern exposure I'd guess there's a decent chance for re-growth where the leaves dropped. In any case, you'll know by Memorial Day and can prune out any dead branches then. As with the new ash tree, keep it well watered and mulched and use root stimulator to help it get well established before next winter.
Another general rule: if you fertilize, it's a good idea to stop feeding trees and shrubs 6wks to 2mo before the first freeze is expected since you don't want to stimulate new growth that won't be "hardened off" before the freeze. This also gives the plant a breather so it can store energy before it goes dormant for the winter.
Good luck!
You should come to this thread if you are interested in gardening. I'll post a link there to here. Maybe someone can help with your question.
http://www.freerepublic.com/focus/f-chat/1341811/posts?page=643
Becky