I have a royal gramma and a sunrise dottyback in the same tank, and they have been fine for about six months. I was ready to yank the gramma and put him into the nano if they fought.
I think the key is space. I have 100 gallons and tons and tons of LR
so they don't even see each other much. The gramma has his space, and the dottyback has his, and they don't mix much. The gramma is 2" and the sunrise is 5".
Diadems are much more aggressive, I have kept these before and like them. I have not seen another fish, except perhaps the purple pseudo that at one inch long could run off a fish 4 times larger than itself. Try putting one in a clear plastic breeder box inside the tank and see if the other tries to attack it. The plastic breeder box will protect the fish and you will have a clue. I used this to introduce my male maroon clown to my large female. The smaller male lived in the box for about a month before she tolerated him enough to let him go into the tank.