Originally Posted by lairpie
No one is better able to tell you whether a +heal boost once every 2 minutes that's going to be completely useless the vast majority of the time is more valuable than a large self heal on demand than your resto druid is. If he has really good situational awareness and reaction time, he probably doesn't need it, but no one is more able to decide that than him. In a fight where there's no chance of dying, obviously eotm's use is better than the extra 4 healing. I'd say though, if you die on a fight once out of 50 pulls where having battlmasters would have saved you, its better than EOTM unless there's a very distinct time where you're going to save the use effect and use it then for some huge benefit. If you want some only partially serious math, any time chance of trinket saving him * his +healing > eotm's average healing - 88, its a good bet. 2600 * X = 133.5-88 X=1.75%. So, if there's a 1.75% chance that Battle masters will save him, its as good as the average amount of +healing gained from eotm. Obviously people can argue that on use +healing is far better than the average or far worse than the average, and you can argue that I should count some amount of benefit from the time I was alive, before I died, but really the point when it comes down to it is does battlemaster's have a better chance to save the healer or does essence of the martyr have a better chance to save someone.
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At one time I had both of these trinkets and began to realize that I very rarely used the Martyr, but I was pretty good at using the Battlemaster trinket. If your druid has this problem too, he may prefer Battlemaster since it is definitely easier to remember to use (especially if you do arena). I ended up macroing Martyr to swiftmend just so I would actually use it, which helped me.
Anyway from a theorycrafting perspective, lairpie's analysis is pretty much how I see it. I would emphasize, though, that if I had to pick one I would only use the Martyr over the Battlemaster if there was almost no chance of dying. I don't think clickable +healing complements our style of healing very well (reliable hots, raid maintenance with regrowth, emergency healing through swiftmend). It helps swiftmend, but not so much the other two. It won't reliably add to hot tick sizes, and regrowth's direct heal coefficient is not very good anyway; haste is a better stat for it. Clickable healing is not worthless for us, obviously, but I believe it isn't worth as much as passive healing, and in this particular case the added protection from dying due to the Battlemaster's HP boost probably wins out if there is even a slight chance that you will die and cause your remaining healers undue hardship.