Why do some trees in California have dead brown leaves but also new green leaves?
Whether trees are deciduous or evergreen, their leaves don't last forever; they need to be replaced at intervals.  The process of photosynthesis depletes the chlorophyll in the leaves, so that needs to be replaced and this is a significant metabolic cost to the tree.  Therefore, whenever a tree is experiencing metabolic stress, it will slow down the chlorophyll replacement, and let the leaves die to save energy. It's metabolically cheaper to simply let the leaves die -- after removing the most precious nutrients -- and then regrow new leaves as needed, than to keep repairing the leaves that aren't needed because the tree is resting for other reasons.

In temperate areas, where there are well-defined seasons, this typically happens in the fall, and deciduous trees let their leaves die all at once in the fall.  In tropical or subtropical regions, where trees could photosynthesize all year, leaves may drop all year round (as with evergreen trees, like conifers, in temperate regions).  Often, though, their leaves will reflect metabolic stresses on the tree, such as drought. 

(The Wikipedia article on "Deciduous" makes the point that this can be very localized, related to very local environmental differences that could only affect a single tree.)

Much of California is a subtropical region, and it has been experiencing severe drought for some time, so it wouldn't be surprising for a tree to have reached a point where its leaves have all had their chlorophyll removed.  On the other hand, as the El Nino event of 2015 increases, rainfall in California is returning, so it would also not be surprising for a tree to have recovered from drought enough to start making new leaves.  

If your question is why the old leaves didn't fall off before the new ones started to regrow, it is probably simply a matter of timing.  The tree doesn't really "care" if the leaves fall or not, so long as they're not using up its resources, so there's no reason to force them off.  The new water supply may have arrived fairly shortly after the degree of drought that caused the tree to shut down the leaves.