My vote goes to the Tanking Chest first. If i remember right, the Chest piece drops in T13. So unless you are in one of the super raid FCs, you won't be getting that anytime soon.

I normally go for the Left side first, like Robin said, you get Str and Vit on your left side. Right side only give Vit. I suggest you to farm ST like crazy for ilevel 100 gear for place holder gear, while farming Soldiery to get a complete set of ilevel 110 gear. After i upgrade all my tanking gear to 120+ all my ilevel 110 gear will go to my Gladiator retainer who gets all my old tanking gear.