Both are RNG, LFR is one chance a week per boss to get loot, you have a chance at getting a Burden every time you participate in killing a rarespawn on the isle, you have a chance to get a Burden every time you open a loot cache chest (the gambling "minigame" with the Hozen in the cave), and you can guarantee a Burden every 50k Timeless Coins, plus you get 1 guaranteed burden from a zone chest.
Assuming efficient Timeless Coin farm, it would not be hard to farm 50k coins for one Burden per day- Ghost Ship and Evermaw spawn every hour and reward nearly 1k coins each, so that's 2k coins per hour from them alone. Filling in the time between Ship+Maw spawns by killing the Ordos yaungol that spawn from repeatedly using Scroll of Challenge, especially in a 5-man group, was netting my guildies and I about 3k coins per hour at our kill rate.
So, that's one guaranteed Burden in approximately 10 hours, with a chance to get a Burden every time you kill Ship or Evermaw. Burdens can drop from the yaungol as well. So, assuming you do this each day, you can get 7 Burdens a week, minimum, fairly easily.
LFR, on the other hand, is about a 3-6 hour investment once per week at current clear times and does not guarantee a loot drop or upgrade.
Sure, it takes less time, but it's probably for less reward and certainly for less reliable reward.
I spend a few hours a day on the Timeless Isle, and I've gotten in excess of 10-15 Burdens on a single character since 5.4 launched. I've done LFR every week on that same character, and I've gotten 2 pieces of loot so far.