They are both supernatural. You know... Ghosts... Gods... Grim Reapers... and so on.
In both dramas we have 2 couples. AATM has love triangle but it's not very strong but Goblin has none.
AATM has mystery and suspense but Goblin doesn't.
Goblin is way more hilarious than AATM.
Acting in both is superb.
They both have bromance but the bromance in Goblin is more sweet. hilarious and strong.

They are both supernatural. In Gumiho, the main girl is not a human and in order to become one she needs a human. She is +500 YO.
In Goblin, Kim Shin is not human too. He is +900 YO. He wants to end his immortality. In order to that he needs a human bride.
Goblin has more interesting storyline and has a strong sweet bromance too.

The leads are the same. Sang Doo is the first main role for Rain and he acted very well. Rain acted a father who adored his daughter and his love in both dramas. CBM is more hilarious than Sang Doo. They don't have same plots and Rain's character in Sang Doo is more miserable.
Both dramas are must-watch! ;)