Blade of ruined king vs blood thirster.

Do you need to get through a bunch of beefy tanks? Bork. Do you need to survive burst by having a big shield at the beginning of the enemy combo? BT.

Do you only have one attack speed item? Probably BT. Do you have two or more attack speed items? Bork will get extra procs.

Do you need to be able to kite with the active? Bork. Do you need to be able to stand still and drain tank? BT

Do you have runaans? Probably bork as it applies the passive on bolts.

There really isn't a definitive best answer, especially considering that there are times that each different life steal item is the most optimal

blade of the ruined king is usually good vs tanks for the on hit % passive, blood thirster vs burst champs, that shield is pretty good

get both

and have tons of life steal, and the passive shield and the bork passives and all the stats of both.

can never go wrong with lifesteal, attack speed, ad, shield, active, % hp damage

Both are good for different things.

BorK is good if you want to auto a lot. Think Ashe, Kalista, Tristana, or laning Yi. They want to auto you a lot to do more damage, because they already have on-hit effects to apply. It's good for champions that want to kite and lack high mobility (as it steals move speed. Think Ashe, again). It's usually the better choice if the enemy team has a lot of tanks, because of its on-hit effect.

Bloodthirster is better if you are going for strong autos. It gives a lot of AD - tied only with Death's Dance - and gives the most sustain on a single item. It works best on champions like Jhin or Draven, who don't hit as fast, but hit hard. It's a general sustain item, and does best against other DPS champions, although its shield helps a lot against burst.

And, the one you missed, Death's Dance. Its sustain is best for ADC casters (that still do primarily physical damage. Sorry, Corki). Think Xayah. They typically can't sustain off of their big damage (as it's usually an ability or an AA enhancement not covered by lifesteal) with the other two options. It does best if the enemy team has an assassin, as it lets you actually survive their burst, and gives you an attempt to heal back up.

AD casters build Death's Dance because it gives cdr, higher AD and health from landing your abilities. Autoattackers build BoRK for the attack speed and powerful on-hit effect.

Bloodthirster currently has no reason to be built.

If you need dps Botrk. If your champion has better on hits botrk. If they have tons of hp tanks get botrk.

If your champion has better AD scaling get bloodthirster. If you need just a little more hp to survive get bloodthirster for dat shield.

Note: crit strike counts as scaling. So having 2 zeal items plus IE could mean bloodthirster is a better item. At that point it depends entirely on what you need. Are tanks what you're having difficulty killing (botrk)? Or squishies (bloodthirster)? Are you dying too fast (then get bloodthirster)? Or do you need some extra kiting (botrk)?