Both dramas feature a male lead with mysterious powers, solving cases.

Im Wu Xin the male lead is immortal, but doesn't know why.

In White Cat Legend the male lead is a cat-person, and also doesn't know why.

Wu Xin focuses somewhat on romance, while WCL focuses more on friendship, and camraderie.

Both male leads wants revenge on the female lead for something they did in a past life. And both male leads have wandered the earth for hundreds of years, waiting for an opportunity to exact that revenge on the female lead when she is reincarnated.

Both feature male leads from another world with supernatural powers, whom the female lead is able to summon and order around.

Both male leads are "coma ghosts" and only 1 person are able to see and communicate with them.

The Ghost Detective is more a thriller/mystery and has a darker tone.
While Ghost Doctor is more comedy oriented and is much lighter in tone.