I take value proposition to mean criteria used by a purchaser to determine which aircraft to buy. Excluding financing deals and fleet commonality, the main criteria used when purchasing an aircraft are capacity, range, and seat mile cost.
3 class capacity of the 767-400 is 243 vs 301 in a 777-200er.
range is 5600kt vs 7000kt respectively.
seat mile cost is 7 cents vs 7.5-9 cents respectively. source
Seat mile cost is trickier as airlines do the reports and they use different criteria. You would think that a larger plane would have lower seat mile costs, but configurations differ between aircraft, airlines, and trip length. You are also looking at the largest model of one series, usually the most efficient, and comparing it to the smallest of another, usually the least efficient. It's kind of a mess and the manufacturers argue about this all the time.
The upshot is that the 767-400 is better for thinner (lower passenger demand), shorter routes and the 777-200er is better for longer, thicker routes where the increased cost matters less, as the 767-400 can't do the job.