I have two tanks , a dh and a dk , i have tanked mythic nh and tons of mythic+ with both of them at high key lvls , i have to admit that dk is leagues above dh , lets see why:
Dk pros compared to Dh
1. DK has much better trash management , Dh has no tools to control chaotic situations while dk can just use his blood boil or gorefiend grasp and get everything under control asap , blood boil is MUCH stronger at sustaining aggro compared to sigil of flame or glaive , literally this hurts a lot at mythic+ , sometimes someone ninja pulls or trash are spread and there is no way to take control of all of it fast as dh while as dk its very easy.
2. DK has a combat ress while dh has not
3. Dk has death grip which is extremely usefull on some occasions
4. Dk has better cooldowns and mitigation , i feel immortal with my dk , i tanked a +10 hov stone this reset after healer left the group before first boss and finished it without dieing very easily at 905 ilvl , literally someone even pulled the trash at hyrja and had to tank both the boss and trash and managed to do it without healer. I cant do something like this with my Dh , his cooldowns and mitigation are not weak by any means but they are leagues below dk ones and they are also fewer.
Dh pros compared to dk
1. Dh has better dps than dk , i pull around 500k ST and alot more even up to 900k aoe with my dh , this is alot of dps and im only 903ilvl without a 2nd legendary and i use stamina and versatility trinkets and stamina flask , this is all thanks to spirit bomb buff and its one of the only advantages dh probably have compared to other tanks and they try to take this away now which is stupid because in that case there is no reason to play a dh anymore. Dk can still pull alot of dps with rune weapon and appropriate trinkets/legendaries.
2. Dh has a cc , imprison can make a difference but that happens rarely , its useless on raids and marginally usefull on dungeons.
Overall , i think utility wise dh is very weak but i can only compare him to my dk , i dont know anything about other tanks , his dps is the only thing that makes him shine and when they take this away , it will be pointless to play a dh tank.