I’m not a huge fan of the BoA gear that drops on the Timeless Isle. I find that most of the gear to have bad stats overall and occasionally being exceptionally misplaced, even if you have the correct spec picked. For instance, my warrior received equipment that contained haste as the only secondary stat. That said, after reading a few forums on the BoA gear, I’ve been thinking of where Burdens of Eternity are optimally utilized.
The problem with the BoA gear is that the stats generally are pretty horrid. You may not necessarily receive the best stats on an item so you have to carefully select the items for upgrades. My preference is to prioritize non-tier pieces and trinkets for Burdens. So rings, necklaces, belts, bracers, boots and capes make for the best possible upgrades. With LFR and Celestials available (if you prefer not to do Flex or more difficult raiding), these items provide enough of a boost if you’re in desperate need for ilvls. Belts and capes can be further trivialized if you can afford or craft a belt as well as possessing the legendary cape.
One thing in reading the forum post regarding Burdens of Eternity is that Blizzard does not want you to instantly get the best item for your class/spec. There is a huge randomness factor which is a big gamble. So you’ll have to farm a bit or focus on the treasure chests in that room in an attempt to grab a Burden to get an optimal one. So keeping extra, uncrafted items is a good idea in preparation to reroll your Burdens (as infrequent as they may come).
Either way, don’t depend on these items to put you over the top as great items. They still are throwaway items for the most part.