Consider all aspects, damage to heal ratio, the damage alone itself, in team fights in terms of speed or maybe 1 on 1.
make sure to vote in the pole and state your reason why, thanks.
You can also mention certain champions such as 
that might benefit from one or the other or in general for all/most champs.
or
First thing is those items don't do the same things, so comparing the damage output from them doesn't make sense. Infinity edge, on it's own, is just crap cause it needs a zeal item to make use of the passive unless you are playing a specific champion like Yasuo or Tryndamere who have crit in their kit. So, if your teammate is rushing Bork into IE, they're seriously missing out on the damage that a zeal item would give them over the Bork lifesteal.
One thing people forget is that items are conditional. Some champions will build pretty much the same items every time you play, but there are some that need to alter their build path entirely.
When I play , for instance, I generally go 
-> 
and finish and then the rest of the build goes from there. However, if I'm getting stomped in lane by maybe a 
or 
(which shouldn't happen but whatever), then I may swap for an 
so I can benefit my team more. I personally like on Ashe, but if they have a ton of tanky teammates, may be a better choice. Or, if they have a ton of CC, then I'll go 
instead of either. Then I look at the items the enemy is building. Do they have armor? Yes, 
it is then. Do they have lifesteal or sustain from their kit? Yes, 
should help with that. No, well then let's go 
. If their team hasn't built any armor yet, I may either get 
if they have AP burst, 
if AD burst, 
if I'm getting solely focused by multiple people, or for more dueling potential plus crit and attack speed. Additionally, I could build 
instead of to get MR and Attack speed, which both work well on Ashe and the magic damage on hit makes her still do damage if the enemy starts building armor (not tons of damage, but still some).
As you can see, from that paragraph alone, I just listed 13 different items that Ashe could get that all depend on the match up she's in. There really is no "buy these all the time" items. People have their core, but even then, everything else is secondary and situational.
If you are playing as a splitpusher, than I think the would work well on him so more than one person has to come to answer the splitpush, but he also needs a cause it's beneficial to his kit.
might work on a champion like 
cause bork gives him the sticking potential so he can finish off the person he's after and IE gives massive damage, but again, he needs another item like to make full use of the IE passive and to deal with the fact he's a melee champion who needs to get in range of people to do damage.
Ignoring outside sources though and only getting these 2 items, I'd rather something one cause the lifesteal plus damage reduction would help them out in a fight a lot more than relying on the RNG gods to save you.
It depends on the champion. Some champions would want some, some would want the other. Bloodthirster is generally good as a later item so that your massive damage can net a good chunk of lifesteal. Dancer is a good item in general. BOTRK is generally only good against tanks and only really works on certain champions. IE is a good item for most of the champions that can use it, although it's not always a primary item.
