How to update apps in iTunes 11.3?
This is for iTunes 11.4, but I think it's the same in 11.3 and other versions around here, for anyone looking.

I had this issue too, because there isn't enough space on my iDevices to update in place.

Open iTunes, make sure you're in "Library" and not the Store.  At the top left there's a drop down menu, it defaults to "Music".  Use it to select "Apps".  Then in the top center area below the status box that shows sync progress and the like is "Updates".  Click that, then "Update All Apps" in the bottom right of the window.

Presto, utilizing your computer's network connection and hard drive for better app updating.