This is extremely theoretical. In the game, you have to factor in the gold value of each stat, and in actual practice, you can only get health and armor in preset amounts from items.
Sure, theoretically if I have 1500 HP and 200 armor I would rather have 500 AR than 500 HP. But I can only buy so much of each stat with the amount of gold I have. I can't easily buy 500 AR, but I can sure buy 500 HP. Even if I could buy 500 AR, it would cost me a ton of gold and item slots that would've been more effective if I had put them towards HP.
Example: I have 1500 HP and 200 AR.
EHP (effective health against physical damage) = HP * (AR/100 + 1) = 4500.
For 3000 gold, I can buy
+
+
OR
.
+
+
: HP = 1500, AR = 330. EHP = 6450.
: HP = 2300, AR = 200. EHP = 6900.
Obviously,
is far from ideal in this case, even with the 
. This is because 3000 gold can get me a lot more HP than AR.
Note that the ideal combination of stats is probably something else. For example:
: HP = 2000, AR = 260. EHP = 7200, higher than both.
At higher HP levels, say, 3000 HP with 150 AR, you probably want to go with AR. At lower HP levels, you want HP. The relationship isn't that simple.
Essentially, you are limited by the gold value of the items, and by the actual preset stats you get from items. In further practice, you have options like passives, actives, or other stats like CDR that you might want from the items. You also have to consider power spikes, your future build path, and what the enemy team's composition is. For example, armor might be the slightly more effective option against physical damage in a certain case, but buying health could be a significantly more effective option against magic damage, and you might need health to survive the mage.
There's a lot of decision making that goes into building a tank, and you have to weigh your options rather than rushing a Thornmail every game. It would be very sub-optimal.