What are the advantages of specialization in 3.3?

My Disciple of Hand classes are just now reaching the point where I can specialize in crafting disciples. However, as I am limited to three specializations, I'd like to know what the benefits are for each class before I choose.

Many of the existing guides are from the start of the expansion and there have been tweaks over the patches where some specialization items can now be crafted by anyone. It also doesn't seem like the special specialist abilities make a big difference in being able to craft HQ items.

So what remains special about each class's specialization? What benefits would specializing in a particular disciple bring?