While these shows don't have anything in common plot-wise, they have a similar origin: they're both manga from the 60s and 70s that got a "modernizing" reboot in 2018.
"Modernizing" because while the story, characters, and pacing are kept untouched, they're both re-set to our days, updating also the conflicts and the criticism made to society to make it match with today's problems.
Both series involve a human partnering with a youkai in order to fight other youkai. Ushio to Tora, however, has the added dynamic of the two leads being at odds with each other.
They're also both recent adaptations of older manga, and have sort of similar visual styles, though Kitarou's source material is MUCH older than Ushio to Tora's.
Both have this "childish" character design, Both have this supernatural theme and a human girl that follow the protagonist, Both of these two are based in a classical manga
The difference is:
Dororon is more like a comedy show, and gegege no kitaro is more a adventure show