black cleaver
1850 + 415 + 800 = 3065g

Infinity edge
1850 + 975+ 880 +375 = 4080g

Both gives 80dmg. The bonus effects are arguable ,

stacking -12 armor per hit that gives the whole team dmg. they seem to die about 20%-30% faster (after spending 800g upgrades)in practical teamfight in my testing.
vs
20% crit that also effectively make ur crit x1.5.

i could have gotten like +40% atk speed with that 1k gold that also goes into making an item with gives another - 25 armor.

Its a surprise the black cleaver has not being nerfed yet, but i'll continue abusing it over overated edge

Both do 80 dmg, but infinity's edge passive is awesome. Especially on Ashe or other chars with crit boosts.

BTW :
Black Cleaver is 80 dmg and a good armor debuff passive
Infinity Edge is 80 dmg, at least as good passive AND 20% critical.

The 20% crit is definitely worth the 1000 extra gold, especially as it comboes with the passive.

BTW, why choosing ? Get both.

its 1k gold we are talking about, i could have gotten the black cleaver much earlier or have another 40% atk speed if i had the extra 1k gold.

the occasional crit does not justify costing 1k gold more. I found black cleaver consistently performing much more bang for the buck. By the time u gotten inf edge, ur opponent will have gotten another 500+hp that u have to deal with.

Unless u have so many other crit like from runes or other items. 20% crit and 50% bonus crit is not anywhere close to -12 armor stacking and 40% atk speed

both give 80 damage, the 1k cost is around about the cost of the 20% crit chance, about 100 over

50% x Crit% bonus damage vs 12 armor reduction stacking 5 times

depending on what else you have, and who its on, they seem around about equal to me, infinity having the disadvantage of taking longer to get

The problem is, there are a number of different variables to consider here.

Black Cleaver is great if your target doesn't have too much armor. When I buy an item, I try to consider the % damage output it gives at that point in the game over not taking the item. The more armor my opponents have, the less effective the passive from BC is.

The thing about Inifinity Edge, the bonus crit damage is scaled. That's right, it always gives +50% base damage again regardless of what point in the game you are or what kind of armor your opponents have. If you have 50% critical chance (not hard to get), that's on the average +12.5% extra dps. Not too shabby on top of the +80 damage (which by the way gets counted towards the crit).

Finally, there are the numbers and there is what actually happens in-game. Most games I don't bother with crit because the chances are so low. In LoL, it's ridiculously easy to get over 50% critical chance. This means, at least every other hit is going to be a crit! With Inf. Edge, this means I'm doing 2.5X normal damage! During an actual game, you sometimes only get one more hit on a target and then your chance is gone. The chance you'll do a 2.5X spike and make the kill totally skews the game in favor of increasing a single blow. In my opinion, this gives crit % and + crit damage items something of an edge over increased attack speed items, or items like Black Cleaver that require that you get a few hits in before you start seeing benefit from the passive.

Just as a side note, it seems to be generally acknowledged that the two required items for a physical dps are Last Whisper and Infinity Edge.

It all depends on the situation.

Certain champions love crit because it synergizes with their mechanics somehow, and these champions will usually buy a lot of crit. But others synergize will with Black Cleaver, with the shining example being Corki, but Teemo, Twitch and other fast-hitters like it as well.

Last Whisper is in no way a "necessary" item by the way, it's just generally good because there are usually some people who run around with way too much armour (Taric, Frozen Heart carriers, Rammus etc).