Looking at your armory, I'd say use both. The Shado Pan trinkets is pretty garbage for destro as haste procs do very little.
Find a way to keep track of both procs and for UVLS refresh Immolate during the proc. Try for 2 casts if you have enough time. If not, one Immolate plus a Conflag would be the best use of it, especially if it's a FnB Immo/Conflag on a larger pack.
For Yulon's Bite you'll want to have the AD talent and pop DS every time the trinket procs and refresh Immolate (unless it's under UVLS at the time) and then dump 4-5 CBs, making sure to refresh Immolate before you lose all that crit.
Thanks for the help guys. I'm gonna try running both of them. I plan on going demo once I can get around the 8k haste caps, but I suppose now for destro, I can run both of them simultaneously and see how it flows.