I always. ALWAYS. go bloodthirster. You HAVE to have that sustain because people will be poking you left and right with their skill shots. Or in case of a bind and bruiser decides to come and try and come from behind you need a bloodthirster to survive. I never count on my teammates to peel them off of me.
+ Not to mention that its damage stacks, meaning more damage than an IE.
you go IE if you're losing, BT if you are winning. BT is early damage and sustain + dueling power so you can try to make things happen midgame, IE is a more late-game oriented purchase. Buying a BT when you're behind won't help you win back any lost ground (especially if you are dying), while an IE doesn't consistently crit enough or give as much AD or lifesteal, requiring more items to be fully efficient.
If you read this signature, then that meant that I had control of what you read for 5 SECONDS!! http://imgur.com/n8yh1
with an insert GA/Warmogs somewhere in there., usually after IE.
Getting the avarice blade gets you a surprising amount of gold by the time you turn it into an SS. 35 minutes in assuming 100 creeps/10 minutes is 1k gold(360 from gp10 and 600 from last hitting). You just paid for a giant's belt that the opponent doesn't have.
Not to mention if you end up dueling bot with ult up, getting a crit means free win, and you'll usually get 2-3.
What do you do when faced with two choices? Simply toss a coin. It works because in that brief time that the coin is in the air you know what you're hoping for.