Reading discussions like mmo-champion forum threads, gives me a strange sense that we have entire culture of tanks clashing, with avoidance tanks carrying themselves a lot like french nobility, sophisticated and demure, believing in supremacy through class. Their attitude towards stamina tanks seems very much like talking to hicks and hillbillies. Of course, this is not true but the general attitudes are fascinating :)
So, which side is right, which is better?
I would like to say that everyone are born equal but this is not true. Sadly, stamina tanks are just more reliable than avoidance tanks. The answer lies in studying current raid design, with bosses that hit massive. Anyone who has been tanking Ulduar hard modes know how much damage is flies around with bosses like Freya or the Assembly of Iron.
The general rule is that you have to be able to survive at least two boss hits without a heal. Shrewed but so is life. With Freya's hard mode, the hits that she lands on you are consistently around 18k. That means that as a tank, you much have more than 36k health after all the raid buffs, along with a healthy sortment of cooldowns because extra damage from ground tremors.
A tank with 39k health can survive this no problem. An avoidance tank, with 35k health will dodge most of the hits, but that is like playing russian rulet. Eventually the minority occurs and he will take two hits in a row, quickly dying, taking rest of the raid with him. This is what it essentially comes down to and each time the stamina tank is simply more reliable.
From a healer's point of view, this is even more desirable because healers like predictability. As a death knights, I'm no strange to healer-rage about taking heavy spike damage, so this is especially important for me. Avoidance tanks are prone for a lot more, big spikes of damage that can lead to unnecessary wipes, even in easier raids or even heroic dungeons, if a healer is unable to react quick enough.
And before you spam my mailbox, shouting that it doesn't happen with good healers, do not bother. I have been tanking with healers of all shapes and colors, so I know it happens more often than some like to admit. The same story is told by many avoidance tanks, feeling unfairly treated when they are removed from raids because of low health pools, even if they have the achievements to proove they can do it.
However, you cannot blame this on raid leaders. An experience raid leader wants reliable tanks. Running with an unreliable one is like driving a car with nitroglycerin for gas; could blow up at anytime and even more with pugs, can blow your raid up along with it. In the end it also just comes down to raid design and Ulduar is a prime example of this; an encounter's difficulty curve is not so much in the mechanics, but just in surviving the massive damage.
Take the hard mode of the Iron Council; once only Steelbreaker is left, it comes down to a dps race. The tanks literally sacrifice themselves to buy that time for them, with the first tank blowing his cooldowns until he blows up and then the second tank does the same thing. There, if you do not have the health to survive, you are useless and this is true for most Ulduar encounters.