Who do you trust?
As a retired and now amateur techie I have been reading what I can since this issue raised its ugly head and in trying to boil it down to the essentials I think it is about the balance of trust and control.
- DoH bundles DNS calls into the same ports as encrypted HTTPS traffic and observations by network admins can't see or control what is going on
- DoT encrypts DNS calls. Admins and indeed anyone else with authority will not see the content of those calls but can see who is making them and track the effect.
Living in the UK, given a choice I think I would opt for DoT. It would make it more likely that admins can run a reliable network. I have reasonable confidence that any of my web searches or connections to sites that give me information about, for example, the wisdom of Brexit will not result in a visit from the fingernail removal men.
If I lived in a less stable society and were trying to find information about alternatives to my currently "elected" president/prime minister who wants the job for life I think I would choose DoH.
It comes down to your point of view.
An analogy. I read Theordore Rockwell's book about US Admiral Hiram Rickover and his key role in the development of the their nuclear submarines. There was a debate over the safety vs maintenance balance regarding possible leakage from the PWR design reactor with just a removable gasket sealed cover which gave better access, or adding welding the whole thing shut on top . Navy engineers wanted easily removable lids with gaskets. Gaskets suppliers emphasised the quality of their product. The general consensus was that removable lids with gaskets was a good idea because the benefits outweighed the risks.
Rickover asked a different question of those involved.
"Suppose your son were to serve on this submarine with his life dependent on its safe operation. Would you let his life depend on the continued integrity of the gasket to hold back every droplet of the highly radioactive water? or would you rather have a weld backing it up just in case.?"
They all changed their minds and opted for welded up lids.
Generally, when the benefits to me outweigh the risks to you, I will opt for the most benefits. When both the benefits and the risks apply to me I will tend to minimise the risks
I am fairly sure that DoT is the better solution but if pushed I would opt for DoH.