Both Ram options you have chosen are compatible , I have a Qualified Vendors list for the Asus Z77 and both models are on it , therefore you won't have any issues with them at all.
Comes down to price really and what you think is value for money, personally I would go with the 1866 as it may give you some extra punch, nothing wrong with getting the faster option , but it depends on how much you wanna spend , the 1600 will do just fine.
I'm willing to buy the 1866 if it is faster than the 1600. But it's just the timing is higher for the 1866, so I'm kind of confused. Care to explain how the timing affects RAM speed for this memory newbie?
Btw, where do you see the Qualified Vendors List?