According to an article in Forbes magazine, zoos nowadays are trying to avoid mixing African and Asian elephant populations.
The reason has little to do with personality differences and more to do with health. African elephants can carry a virus called EEHV without complications, but Asian elephants can die from it.
Asian and African elephants can accept one another and become like family despite their size and personality differences (Asian elephants are smaller, only males have tusks, and both sexes tend to be less into rough housing as their African cousins).
Interestingly, Asian and African elephants have differences in communication sounds/body language, but when placed together, they seem to learn each other’s methods and combine elements of each to communicate successfully with each other.
Photo taken at my zoo