There are three main factors for the whole discussion which can/will led to different results.
a) raid size
As we all probably already know 25M bosses hits WAY harder, so having a 10% buffer there can be much more worthwhile than a 10% buffer in 10M. I for myself can only state from 10M experience in the last ~ three years, just wanted to make that clear before hand.
b) healers
I could argue about their healing styles (proactive vs. reactive) etc pp but let's just assume they know what they're doing and the can anticipate what you're about to eat and use their heals accordingly. What will greatly differs (even on a 25M vs 25M or 10M vs 10M comparison) is the class combination.
I raid with a disc priest & a holy paladin (fairly common combination for 10M), me healing taken regulary looks something like that:
0. (shield barrier)
1. Beacon of Light
2. Atonement
3. Illuminated Healing (paladin mastery)
4. Powerword Shield (to procc rapture)
5. Chi Wave (from my co-tank)
6. AoE heals (prayer of healing, spirit shell, divine aegis)
7. Eternal Flame (fire and forget 30s hot from holy paladin) + Holy Shock
8. other selfheals (enraged regen, victory rush, impending victory, healthstone)
As you can see in this particular setup there's not much attention on me (and in fact my co tank needs just as much if not more selfheal to stay alive, spamming purify, expel harm, etc) or directed heals. While we regulary eat the most damage there's just enough raid damage going on to keep us alive with some additional love from instants/hots. You could argue that having more total damage reduction lowers the amount of smart heals we'd need (via Atonement) but i think you got the general idea. There's just no room for a scenario when a healer has to decide between using a heal vs greater heal on me unless things goes downhill (somebody screwed up on a mechanic, we timed our personals bad for predictable bursts, etc).
c) bosses & approach ('tactic')
There are several ways to beat an encounter from solo tanking it over kiting things to the Vaelestraz room to ...
So let's see: Last tier there were two bosses in particular who could give me a headache on 10M, Mel'jarak and Shek'zeer (heroic mode). Both could literally "instagib" me between two heal casts when my shield barriers dropped. Having considerable more health allowed me to survive one more unmitigated hit.
On Meljarak we liked to CC the puddle throwers so i still had to deal with lots of +%haste from the heal casters. Other raids cc'ed some of them because they had the healers (ie: druid, monk) to handle movement better.
On Shek'zeer i tanked ALL of the smaller adds manmode, so they empowered each other and gave me a very good beating (600k+ vengeance), but i had 4 healers to back me up including resto shaman for +10% health. Other raids tanked 3 smaller + 1 big add together or kited some of the smaller ones or used hunter/warlock pets to reduce the damage considerably.
For both cases: i just did what guaranteed my survivability in x out of y cases instead of hoping for the best, the mantra was (and should be for all tanks) gear for worst cases. That's why Theck even started those whole modeling thing, he was afraid to die to a series of hits without much attention of the healers. But this tier is considerable different to the last one: there's just no "instagib" scenario to be afraid of (in 10M).
Possible exceptions
1) Horridon after his buddy dies but that's more to all the other stuff going on and less due his heavy damage on it's own. Our healers have to spend every third global on those dire beasts, if that lines up badly with a direcall/triple puncture/2x melee swing combo... ouch. But he hits that hard that adding 10% or 20% stamina alone won't allow you to survive, in such a scenario you have to rely on personals or just kite him (thanks to Double Swipe you have a decent amount of time to run away).
2) Tortos if you solo tank him, those Bats will heal after you drop below a certain amount of hitpoints (550k, not % based) but if you can bring a third healer instead of a second tank keeping up the crystal buff isn't all that hard with the extra vengeance. As said before, there are some differenct approaches that work just as well (if not better) like kiting the bats or killing them with two tanks which adds a noticeable amount of control (stuns), cooldowns (personal + external) - so just saying x is king there can be plain wrong.
tldr; at least for 10M it depends on how you handle things, with high enough itemlevel (52-something) and the option to change to stam trinkets for nonblockable burst-heavy fights like Megaera, Council, etc i just don't see a clear reason to stick to a stamina overload when i'm not in the danger of dying and mastery on the other hand would add both on damage dealt and less damage intake side. Sadly our options aren't just as good as stacking haste or crit and getting both a resource control boost over gemming stam and a noticeable damage increase and we can only hope for some adjustments in the near future but that's still no justificating to dumping *everything* into a stamina when the normal reason for a wipe is failure of a raidmember to a certain mechanic and no tank death. It's not LK all over again when you needed 45k to survive an ability.
The difference is roughly ~ 10.000 mastery from gems & enchants & trinkets which adds up to ~ 6,6% block and ~ 37% (!!!) critblock at the exchange of 9600 stamina or ~ 180.000 hitpoints (before resto shaman buff). And you could still argue about the exchange rates of gems (0.75:1 stam:mastery) versus trinkets (1.5:1 stam:mastery for lei shen vs council pieces) if you want to get the most out of both.