You take bt if your champ scale a lot on ad.
You take IE if you want those super lategame champ (ashe,Vayne,etc.).

Get bt if you think the laning phase is going to be passive and dragged out.

If it looks like theres going to be a lot of mid game team fights/skirmishes then get ie, it will let you deal more damage with auto attacks (beacuse of crits), and you won't have as much time to farm (for bt stacks).

It also depends quite a bit on the adc, and how well they scale with ad.

I build bloodthirster first on champions that are more agressive and need to be close range that need the lifesteal to survive fights (Draven Vayne)
I take IE on champions that should be okay without massive lifesteal in the earlier parts of the game (Twitch Graves)

champions who rely more heavily on auto-attacking (ashe, miss fortune, tristana, kog'maw) due to their kit usually go for the IE. Champions with more skills that scale on ad (graves, sivir, varus) generally take the BT.

IE more damage, and more of an item you would go for if your playing aggressive, and want to continue dominating the lane, BT if your playing passive, and more sustain due to the lifesteal.

Or you can just go for either first, both are good items.

BT -> sustain, later damage

IE -> massive damage

In most cases you'll probably end up getting both, I usually pick bt for the sustain.

I build bt if a champion has more damage from abilities. like varus is almost an ad caster with his q and e burst.

If im getting poked at alot, i get BT first. If i can be more aggresive, i tend to but a VS then get IE to be able to dominate the other ADC