This all depends on what you want to do with the truck. Having owned both an 07 5.9 and now a 2010 6.7, I prefer the 5.9. If you plan to add much power, the transmission is going to be a concern for both. The transmission behind the 5.9 is much cheaper and easier to build than the 68RFE that is behind the 6.7. Also, aftermarket support for the 5.9 is much better as well.
EFI live is available for the 07-09 6.7's though, so that is a big plus over what us 4th gen guys have to work with.
Mileage wise, I was getting about 15mpg on 35's with the stock 5.9. Then it bumped up to 17-18mpg in my with 35" tires after adding a tuner, 64mm turbo, and 90hp nozzles, and all the other basic boltons. I bought this truck lifted, so I dont know what the mileage would have been like on stock tires.
On my 6.7, I was getting 17mpg stock with stock tires. Then added a programmer and deleted the dpf and was getting 20-21mpg on stock tires. Then I added the lift and 35's and my mileage has dropped to about 17mpg again on the highway.
If you are just looking for a great all around truck that will not get alot of performance mods, then the 6.7 is perfectly fine. If you plan to add anymore than about 100-150hp to the motor, then the 5.9 gets my vote.