Kingblade is better if you go ham and repeatedly pew-pew things from medium range. If you're a risk-taker.
Bloodthirster is better if you're playing poke wars - more AD for ratios, a shield that's pretty solid against rival poke, and hit-and-run with an auto is pretty solid with mega-AD.
That said - Kingblade is solid by itself, but a big part of it's cost is in the active and especially %HP shred.
Neither of which scale with critical strike chance.
Trinity Force has a similar issue with Sheen procs and AP not scaling with critical strike chance.
A Tri Force + Kingblade combo can allow Corki's solid mid-game with Tri Force to coast a little further into mid-game, but you're amplifying a weak end-game by getting both in the same build.
If you don't win by mid-game, an end-game anybody with Infinity Edge + Statik Shiv + Last Whisper is going to outscale what a hybrid/bruiser-ish Tri-Force + Kingblade + something else combo is going to offer.
TLDR:
Kingblade if you're a daredevil and risk-taker, Bloodthirster if you like playing it safe.