I've made it clear that I'm horrible with theorycraft and numbers, so no flames! :P
But how much effective health would I be losing or gaining if I sacrificed about one point of dodge (not rating, just one point) for about 200-300 armor? I was trying to figure out what stats I would be gaining and losing with certain gear upgrades, and it hit me that I had no idea how to compare effective health. And can any of you can tell me how I would figure this out for future reference?
Klimpen is right, avoidance is very tricky to compare to Armour or Stamina, and as a result hard to incorporate into an effective health calculation. The reason being is that the value of avoidance is dependent on the amount of incoming damage you receive, and is also random -- when you get hit, it does nothing for you. Stamina/Armour are independent and preserve their relative values regardless of how much damage you are taking.
A good rule of thumb is this: As the damage you take increases, avoidance becomes less and less valuable in relation to Stamina/Armour. The most extreme case would be a situation where you are unable to survive a single hit from a mob. At that point avoidance loses almost all value because the moment you are hit, you will die.
While I can't give you a number, my advice is to just think it out intelligently when deciding between the two. For example, if you are tanking a fast-attacking mob that hits for light damage, wearing the item with dodge would be a smart choice. On the other hand, if you are tanking unfamiliar content, go with the additional Armour until you know how much you are being hit for and how often. Then you can make a more educated decision.
Like Concordia and Venny said. Balance it to your situation.
If you're dodge is already fairly high: Say 17%+ (i say high because 18% or more for me is already awesome and stam/ac/sbv is where its headed now) then sacrificing 1% for 369 EH is quite worth it. If you're dodge is say 15% then 1% is a bigger gain for you than just 369 EH.