My Friend Aestigon used Awakened myth ring 3 til now and upgraded TT ring to 10 like 2 days ago. As a Frost Warden he says hes doing consistently worse in Stage 4 Turtle, because of the crit rate loss and most dungeons feel that way too. Thats Warden tho, low crit rate and 40% bonus to ele dmg and crappy modifier on ring.
Anyway back to the topic u lose absolutely 0 getting awakened myth 3, because if u want the pvp ring u would upgrade the pve path anyway, because of the pvp paths retarded bloodstone cost to get there, arround 100+.
Also Myth Rings no doubt quite an increase for all classes over BT anyway, beside BD/FM(smaller for them, due to high crit rate and 40% ele bonus). Depends on ur class tho and how good ur ring modifier is.
So theres really no reason not to go for it, u will swap to the pvp path anyway from pve path awakened 3. So you can parse for urself to be sure.