I don't know enough about druids. But for warriors and paladins it's not Avoidance vs. EH. Because block is NOT avoidance. It's mitigation. And if all than mitigation is part of EH not avoidance. So stacking mastery is not the same as going for avoidance and ignoring EH.
There are people advocating to stack parry and dodge over mastery, because it prevents more dmg. That's what you do to max your avoidance and follow the avoidance rules.
The question between stamina and mastery is something else.
When you start raiding, you have comparable high amounts of HP but only medicore coverage of the dmg table with block (and avoidance stats to fill them up). At the same time healers struggle with their mana. So block will do both: prevent dmg and increase your chance to mitigate a lot of the incoming dmg. Stacking stamina also increases EH, but does not help your healers (and even if you try it will not make such a big difference anyway, since boss hits are quite small compared to your life as is the HP you can add via stacking. You already have such a hugh pool of health on your gear).
When you start HCs, boss hits will be bigger. So you cannot take as much as you could before. Your HP has not increases as much at the same time, but healers have a much bigger mana-pool. They can afforde those big heals more often. You will have better gear. So you will have a much better coverage of the dmg tabel with your mastery. So chances to block (or even crit block) are high (enough). You will not be able to max the chance to 100% coverage, anyway. Adding more mastery will not prevent much more dmg. You will already block 30% (or more) dmg most of the time. However if you do not bock you have to eat a high amount of dmg. Also magic dmg is increased for some encounters. So it may be a good idea to up your health instead of increasing the chance to block a little bit more. You already will have a high chance anyway via reforging.
When that occurs and if that's the right thing to do, depends on the encouners. There are some encounters that favore mastery all the time. At magic intensive encoutners more health is just better. So as before, you have to gear for what you face if you are doing hc progressions.