Going Full Frame

Hi everyone,

I have been thinking of going full frame for some time now.  My main interest is landscape and not much else.  I have been trying to decide on what would be the best way to get into it.  I can't decide between the 6D and 5D3.  If i go the 6D i can use the savings towards better glass.  If i go 5D3 then it's a nicer body but does it have any advantages over the 6D for landscape photography?  Also, if i went with a 5D3 i may not get as high end glass (at least to start with).

What would you guys recommend in a situation like this.  Thanks ion advance for your input.