So, I'm assuming the reason you don't "just equip both" is you have one of the +def trinkets locked in which makes sense. Even if you can get to 540 without one, they provide a crapton of flexability.
I've kicked around this idea myself. I need a new trinket and I'm sitting on 71 badges atm after buying the Chained Military Gorget. Ostensibly, I'm saving up for the T7 chest but it would replace the Wyrnrest chest while a new trinket would knock off a BC trinket (using the Darkmoon: Vengeance most often there now)
111 stamina is eye popping and I'm old school, clinging a little more tightly to the EH theory than most. I'm sitting at 27.1K hp unbuffed. 600+ hp net gain over the Darkmoon card is flat out sexy.
Note: I am using Seal of the Pantheon in the other slot and sitting at 550 def.
Also, due to the creative gearing I've had to use to thwart the RNG, I'm already sitting at 21.3% dodge. If you're clearing Naxx, that's meh. If you haven't killed a single Naxx boss yet, that number is hot if not bloated already. Adding the Valor Medal would put me at 23% dodge and drop my hp to 26.5K.
Also, also considering swapping in the Arcane Shielded Helm over Tempered Titansteel. With the gem slots, the blue beats the purp and gains dodge while losing a little stam. From the Austere ESD, I gain ~440 armor so its a pretty good swap on EH, and, gain 52 dodge rating, which is the key.
All of this serves to jack my dodge up through the roof and I can reach ~25% unbuffed in about 5 minutes of running around Dalaran and waiting for my JC friend to log on. but all at the cost of Stamina.
Last factor to consider, I am the MT for a 10 man Naxx and the OT for 25 man Naxx.
the obvious answer, using the Pokemon Method is to acquire all of it and interchange it when necassary which leads me back to the "which should I purchase first" dilema....T7 chest or Valor Medal?
your hat may be nice, but I have the little white tank top that says Legendary right across my boobs. I win. (or more correctly, H wins)