The first major difference to note between Dura Ace 7800 and Dura Ace 7900 is - THE PRICE! As of the date of this writeup, just look at the difference between the lowest prices on Shimano Dura Ace parts as listed on QBike:
You get the idea - the Dura Ace 7900 prices are significantly higher than Dura Ace 7800 prices. Why?
Let's go part by part to see what is going on. The new Dura Ace 7900 crankset features a hollow outer chainring, whereas the Dura Ace 7800 outer chainring is a "traditional" solid piece. The inner chainring bolts now affix directly into the outer chainring in the Dura Ace 7900 crankset - meaning there are 5 total bolts - whereas the Dura Ace 7800 crankset has the "usual" total of 10 bolts in the 5-bolt pattern. The new chainring assembly, particularly the outer chainring being hollow, translates to more power transfer from rider to bike. Then, factor in the use of carbon around the crank axle, and you get, as Shimano has claimed, an overall 20% stiffer setup with the Dura Ace 7900 crankset. So really and truly, there some major differences between the Dura Ace 7800 crankset and Dura Ace 7900 crankset, and hence the 180% jump in price.
Next let's consider the rear derailleur. While carbon has been all the rage for many years, trickling down more and more into moving components - most notably with SRAM Red - Shimano has stood firm on using metal. Well, the Dura Ace 7900 rear derailleur is a departure point for Shimano, as they now incorporate carbon into the design. Specifically, the pulley cage and P-body are both made of carbon. And as we know, carbon means higher cost. The other notable change from Dura Ace 7800 to Dura Ace 7900 is the increased range of cogsets that can be used with a given chainring setup, otherwise known as "chain wrap." A rider could conceivably shift into the 53/28 gear combo - with a 12-28 10-speed rear cassette - and it would "work", insofar as there would not be chain rub either front or back. That's not to say someone should ride very long in that gear setup, but it would work mechanically, and the chain would run ok.
Speaking of the chain, there are two very big improvements for Dura Ace 7900. First, Shimano has introduced a removable chain link, just like the SRAM Powerlink, so bicyclists can now drop and clean the chain any time! I have to add an exclamation point because I've been riding the SRAM PC99 series chains forever not only because they ride well, in my estimation, but also because I could easily clean the SRAM chain any time. This is a long overdue change from Shimano, and now I'll be riding Shimano chains again, which will give the ideal fit with other genuine Shimano parts. The second change is that the Shimano Dura Ace 7900 chain is unidirectional. The ramps and pins on the Dura Ace 7900 crankset is such that, for optimal clean and fast shifting, the chain design was best made such that there is an "inside" and an "outside" for the chain.
There are additional key improvements with the Shimano Dura Ace 7900 series components, but these are enough reasons to see why the prices on the "NEW DURA ACE" have jumped so dramatically compared to Dura Ace 7800. Indeed, Shimano Dura Ace 7900 is a new series of parts which shares only the name and heritage of the Dura Ace line of components - beyond that, there are major changes for the better, and as we've seen, a major jump in prices.