Using most cost effective (expensive) items as a gauge of efficiency:
1 Health = 2.58g (Belt)
1 Mana = 2g (Sapphire)
1 Armor = 15.56g (Chain)
1 MR = 15.42g (Cloak)
1 AD = 37g (BFS)
The contender:
Aegis of the Legion: 1925g
BASE:
270 Health = 696.6g
18 Armor = 280.1g
24 MR = 370.1g
UNIQUE:
12 Armor = 186.72g
15 MR = 231.3g
8 AD = 296g
Effective Worth of Base Stats: 1346.8g
Effective Worth of Aura: 714g
Total Effective Worth (Alone): 2060.8g
Efficiency (Worth/Cost): 107%
Total Effective Worth (Two people): 2774.8g
Efficiency (Worth/Cost): 144%
Total Effective Worth (Three people): 3488.8g
Efficiency (Worth/Cost): 181%
Total Effective Worth (Four people): 4202.8g
Efficiency (Worth/Cost): 218%
Total Effective Worth (Five people): 4916.8g
Efficiency (Worth/Cost): 255%
Undisputed Staple Tank Item
Banshee's Veil: 2715g
BASE:
375 Health = 967.5g
375 Mana = 750g
50 MR = 771g
UNIQUE:
Blocks one negative spell every 45 seconds.
Effective Worth of Base Stats: 2488.5
Efficiency (Worth/Cost): 91%
(IIRC, the efficiency USED to be above 100%, back when someone first made the item efficiency spreadsheet. This was also when the cooldown on the block was only 30 seconds. I guess it's been nerfed quite a bit since then)
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Consideration:
Obviously, you have to take into account matchup, team composition and playstyle of individual players when you talk about Aegis. Not every team fight will be 5v5, and not every enemy team is a good mix of AP/AD (although a good team comp usually will spread their damage between the two). Not every one of your heroes will be auto attacking, so they won't benefit the same way from the bonus damage. Even then, Aegis's benefit to you alone has an efficiency of 107%, compared to Banshee's 91%. Then you have to remember that not all tanks need mana. In fact most of them couldn't care less how much mana they have, except for maybe Singed and Blitz. And only Blitz can actually use mana to tank better. Consider how many times Banshee's saved your life by blocking a stun, a snare or Karthus' ult, with how many times it was eaten by a throw away nuke/aoe skill. The number of times the spell block is "wasted" is much higher than the times it saves your life and wins you the game.
Conclusion:
Aegis is, mathematically speaking, potentially the most cost effective tank item. (and perhaps even the MOST cost effective item). The only other items even approaching it's levels of potential efficiency is Guinsoo, and possibly Bloodthirster. Banshee's, on the other hand, can sometimes make or break a team fight. When you buy a Banshee's, you are gambling on that chance to make it all worthwhile.
Aegis: Provides consistent and benefit to you and your team. Can be acquired very early in the game, sometimes on your first trip back if you're doing particularly well. Provides pure tank stats to you and a little bonus damage to everyone else.
Banshee's: Provides situational benefit to you and indirectly to your team. It also builds off of Catalyst, which is a bonus, and it's the only late game heavy MR item with HP.
Side Note:
9x Flat Armor Seals: 12.69 Armor
9x Flat MR Glyphs: 13.41 MR
9x Flat AD Marks: 8.55 AD
Having an Aegis provides everyone near you nearly a full pages of defensive T3 runes, minus the Quintessences. If you think runes are a large factor in how well you do, then the conclusion is obvious. if not, then feel free to ignore this detour.